Network Analysis of cross-border banking exposures¶

The typical structure of an Informatics MSc thesis:

  • Title page with abstract.
  • Introduction : an introduction to the document, clearly stating the hypothesis or objective of the project, motivation for the work and the results achieved. The structure of the remainder of the document should also be outlined.
  • Background : background to the project, previous work, exposition of relevant literature, setting of the work in the proper context. This should contain sufficient information to allow the reader to appreciate the contribution you have made.
    • Keep the sections on Introduction and Background brief. Mention only background and related work that is necessary to understand and evaluate your work. (E.g., definitions what are used later in your theorems/proofs, or data on the performance of other methods so that you can compare it to your results.)
  • Description of the work undertaken : this may be divided into chapters describing the conceptual design work and the actual implementation separately. Any problems or difficulties and the suggested solutions should be mentioned. Alternative solutions and their evaluation should also be included.
  • Analysis or Evaluation : results and their critical analysis should be reported, whether the results conform to expectations or otherwise and how they compare with other related work. Where appropriate evaluation of the work against the original objectives should be presented.
  • Conclusion : concluding remarks and observations, unsolved problems, suggestions for further work.
  • Bibliography.

Projects are assessed in terms of a number of basic and other criteria:

  • Basic Criteria
    • Understanding of the problem
    • Completion of the work
    • Quality of the work
    • Quality of the dissertation
  • Additional Criteria
    • Knowledge of the literature
    • Critical evaluation of previous work
    • Critical evaluation of own work
    • Justification of design decisions
    • Solution of conceptual problems
    • Amount of work
  • Exceptional Criteria
    • Evidence of outstanding merit e.g. originality
    • Inclusion of material worthy of publication

Project Introduction:

  • The cross-border banking exposures are double-edged swords, which can improve the efficiency of global capital and resource allocation, but may also cause cascading contagions to form a global financial crisis.
  • This study will first transform related exposure data into temporal networks with banks as nodes and exposures as links, then perform standard analysis with basic network properties and detailed analysis through community detection by stochastic block models.
  • It aims to gain insights on how systematic risk changes over time and how we can find it, which can finally benefit decision-makers in the financial industry.

Environment¶

  • graph-tool
    • https://graph-tool.skewed.de/static/doc/index.html

Install Graph-tool¶

In [1]:
## packages
import sys
import os
import zipfile as zp

# graph-tool https://git.skewed.de/count0/graph-tool/-/wikis/installation-instructions
if 'graph_tool.all' not in sys.modules:
    print('*** install graph-tool')
    !conda install -c conda-forge graph-tool -v -y
    print('*** finish!!!')

import numpy as np
import pandas as pd
# pd.set_option('display.float_format', lambda x: '%.3f' % x)
import matplotlib as mpl
import matplotlib.pyplot as plt

!pip install --upgrade scipy networkx
import networkx as nx
print("networkx: " + nx.__version__)

import graph_tool.all as gt
print("graph-tool: " + gt.__version__)

*** install graph-tool
/opt/conda/lib/python3.9/site-packages/requests/__init__.py:102: RequestsDependencyWarning: urllib3 (1.26.9) or chardet (5.0.0)/charset_normalizer (2.0.12) doesn't match a supported version!
  warnings.warn("urllib3 ({}) or chardet ({})/charset_normalizer ({}) doesn't match a supported "
Collecting package metadata (current_repodata.json): ...working... done
Solving environment: ...working... 
The environment is inconsistent, please check the package plan carefully
The following packages are causing the inconsistency:

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  - conda-forge/linux-64::py-opencv==4.5.5=py39hef51801_7
  - conda-forge/noarch::pyct-core==0.4.6=py_0
  - conda-forge/linux-64::pygpu==0.7.6=py39hce5d2b2_1003
  - conda-forge/linux-64::pykrige==1.6.1=py39h3811e60_1
  - conda-forge/linux-64::pymc3==3.11.5=py39ha563b64_0
  - conda-forge/linux-64::pyqt==5.12.3=py39hf3d152e_8
  - conda-forge/linux-64::pyqt-impl==5.12.3=py39hde8b62d_8
  - conda-forge/linux-64::pyqt5-sip==4.19.18=py39he80948d_8
  - conda-forge/linux-64::pyqtchart==5.12=py39h0fcd23e_8
  - conda-forge/linux-64::pyqtwebengine==5.12.1=py39h0fcd23e_8
  - conda-forge/linux-64::pytables==3.6.1=py39h2669a42_5
  - conda-forge/noarch::python-flatbuffers==2.0=pyhd8ed1ab_0
  - conda-forge/noarch::python-graphviz==0.20=pyhaef67bd_0
  - conda-forge/linux-64::python-libarchive-c==4.0=py39hf3d152e_2
  - conda-forge/noarch::python-tzdata==2022.5=pyhd8ed1ab_0
  - conda-forge/linux-64::pytz-deprecation-shim==0.1.0.post0=py39hf3d152e_3
  - conda-forge/noarch::pyviz_comms==2.2.1=pyhd8ed1ab_1
  - conda-forge/linux-64::pywavelets==1.3.0=py39h2ae25f5_2
  - conda-forge/noarch::pyxlsb==1.0.9=pyhd8ed1ab_0
  - conda-forge/linux-64::pyyaml==6.0=py39hb9d737c_5
  - conda-forge/linux-64::qdldl-python==0.1.5.post2=py39h4661b88_0
  - conda-forge/linux-64::qt==5.12.9=h1304e3e_6
  - conda-forge/noarch::qtconsole==5.3.2=pyhd8ed1ab_0
  - conda-forge/noarch::qtconsole-base==5.3.2=pyha770c72_0
  - conda-forge/noarch::qtpy==2.2.1=pyhd8ed1ab_0
  - conda-forge/linux-64::regex==2022.10.31=py39hb9d737c_0
  - conda-forge/linux-64::rise==5.7.1=py39hf3d152e_1
  - conda-forge/linux-64::scikit-image==0.19.2=py39hde0f152_0
  - conda-forge/linux-64::scikit-learn==1.1.1=py39h4037b75_0
  - conda-forge/linux-64::scipy==1.7.3=py39hee8e79c_0
  - conda-forge/linux-64::scs==3.2.0=py39hbcdb44f_2
  - conda-forge/noarch::seaborn==0.11.2=hd8ed1ab_0
  - conda-forge/noarch::seaborn-base==0.11.2=pyhd8ed1ab_0
  - conda-forge/noarch::semver==2.13.0=pyh9f0ad1d_0
  - conda-forge/linux-64::shapely==1.8.5=py39h5b5020f_1
  - conda-forge/noarch::smmap==3.0.5=pyh44b312d_0
  - conda-forge/noarch::sortedcontainers==2.4.0=pyhd8ed1ab_0
  - conda-forge/noarch::spectral==0.22.4=pyh6c4a22f_0
  - conda-forge/linux-64::statsmodels==0.13.2=py39hd257fcd_0
  - conda-forge/linux-64::sympy==1.10.1=py39hf3d152e_1
  - conda-forge/noarch::tblib==1.7.0=pyhd8ed1ab_0
  - conda-forge/noarch::tenacity==8.1.0=pyhd8ed1ab_0
  - conda-forge/noarch::terminaltables==3.1.10=pyhd8ed1ab_0
  - conda-forge/noarch::textblob==0.15.3=py_0
  - conda-forge/linux-64::theano-pymc==1.1.2=py39he80948d_0
  - conda-forge/noarch::threadpoolctl==3.1.0=pyh8a188c0_0
  - conda-forge/noarch::tifffile==2022.10.10=pyhd8ed1ab_0
  - conda-forge/noarch::toolz==0.12.0=pyhd8ed1ab_0
  - conda-forge/noarch::traittypes==0.2.1=pyh9f0ad1d_2
  - conda-forge/noarch::typing-extensions==4.4.0=hd8ed1ab_0
  - conda-forge/noarch::typing_extensions==4.4.0=pyha770c72_0
  - conda-forge/linux-64::tzlocal==4.2=py39hf3d152e_2
  - conda-forge/linux-64::unicodedata2==15.0.0=py39hb9d737c_0
  - conda-forge/linux-64::vega==3.6.0=py39hf3d152e_0
  - conda-forge/noarch::vega_datasets==0.9.0=pyhd3deb0d_0
  - conda-forge/noarch::vincent==0.4.4=py_1
  - conda-forge/noarch::widgetsnbextension==3.6.0=pyha770c72_1
  - conda-forge/linux-64::wordcloud==1.8.1=py39h3811e60_2
  - conda-forge/linux-64::wrapt==1.14.1=py39hb9d737c_1
  - conda-forge/noarch::xarray==2022.10.0=pyhd8ed1ab_0
  - conda-forge/noarch::xarray-einstats==0.3.0=pyhd8ed1ab_0
  - conda-forge/noarch::xlrd==2.0.1=pyhd8ed1ab_3
  - conda-forge/noarch::xlsxwriter==3.0.3=pyhd8ed1ab_0
  - conda-forge/noarch::xlwt==1.3.0=py_1
  - conda-forge/noarch::xmlschema==1.11.1=pyhd8ed1ab_0
  - conda-forge/noarch::zict==2.2.0=pyhd8ed1ab_0
failed with initial frozen solve. Retrying with flexible solve.
Solving environment: ...working... failed with repodata from current_repodata.json, will retry with next repodata source.
Collecting package metadata (repodata.json): ...working... done
Solving environment: ...working... 
The environment is inconsistent, please check the package plan carefully
The following packages are causing the inconsistency:

  - conda-forge/noarch::jupyter_server==1.17.0=pyhd8ed1ab_0
  - conda-forge/noarch::jupyterhub==2.2.2=pyhd8ed1ab_1
  - conda-forge/noarch::jupyterhub-base==2.2.2=pyhd8ed1ab_1
  - conda-forge/noarch::jupyterlab==3.3.4=pyhd8ed1ab_0
  - conda-forge/noarch::jupyterlab_server==2.13.0=pyhd8ed1ab_1
  - conda-forge/noarch::nbclassic==0.3.7=pyhd8ed1ab_0
  - conda-forge/noarch::nbconvert==6.5.0=pyhd8ed1ab_0
  - conda-forge/noarch::nbconvert-core==6.5.0=pyhd8ed1ab_0
  - conda-forge/noarch::nbconvert-pandoc==6.5.0=pyhd8ed1ab_0
  - conda-forge/noarch::notebook==6.4.11=pyha770c72_0
  - conda-forge/noarch::notebook-shim==0.1.0=pyhd8ed1ab_0
  - conda-forge/noarch::oauthlib==3.2.0=pyhd8ed1ab_0
  - conda-forge/linux-64::abseil-cpp==20211102.0=h93e1e8c_3
  - conda-forge/linux-64::chardet==5.0.0=py39hf3d152e_1
  - conda-forge/linux-64::conda-build==3.21.8=py39hf3d152e_1
  - conda-forge/linux-64::grpc-cpp==1.45.2=h38f6961_0
  - conda-forge/noarch::ipympl==0.9.1=pyhd8ed1ab_0
  - conda-forge/noarch::ipywidgets==7.7.0=pyhd8ed1ab_0
  - conda-forge/noarch::jax==0.3.14=pyhd8ed1ab_1
  - conda-forge/linux-64::jaxlib==0.3.10=cpu_py39h320bf12_0
  - conda-forge/linux-64::jupyter==1.0.0=py39hf3d152e_7
  - conda-forge/noarch::jupyter-server-mathjax==0.2.6=pyhc268e32_0
  - conda-forge/noarch::jupyter_contrib_core==0.4.0=pyhd8ed1ab_0
  - conda-forge/noarch::jupyter_contrib_nbextensions==0.5.1=pyhd8ed1ab_2
  - conda-forge/linux-64::jupyter_highlight_selected_word==0.2.0=py39hf3d152e_1005
  - conda-forge/noarch::jupyter_latex_envs==1.4.6=pyhd8ed1ab_1002
  - conda-forge/noarch::jupyter_nbextensions_configurator==0.4.1=pyhd8ed1ab_2
  - conda-forge/noarch::k3d==2.13.1=pyhd8ed1ab_0
  - conda-forge/linux-64::libabseil==20211102.0=cxx17_h48a1fff_3
  - conda-forge/noarch::nbdime==3.1.1=pyhd8ed1ab_0
  - conda-forge/linux-64::pymc3==3.11.5=py39ha563b64_0
  - conda-forge/linux-64::rise==5.7.1=py39hf3d152e_1
  - conda-forge/linux-64::theano-pymc==1.1.2=py39he80948d_0
  - conda-forge/linux-64::vega==3.6.0=py39hf3d152e_0
  - conda-forge/noarch::widgetsnbextension==3.6.0=pyha770c72_1
done


==> WARNING: A newer version of conda exists. <==
  current version: 4.12.0
  latest version: 23.7.2

Please update conda by running

    $ conda update -n base conda


INFO conda.core.link:__init__(168): initializing UnlinkLinkTransaction with
  target_prefix: /opt/conda
  unlink_precs:
    conda-forge/noarch::requests-2.27.1-pyhd8ed1ab_0
    conda-forge/noarch::certifi-2022.9.24-pyhd8ed1ab_0
    conda-forge/linux-64::abseil-cpp-20211102.0-h93e1e8c_3
    conda-forge/linux-64::openssl-1.1.1s-h166bdaf_0
    conda-forge/linux-64::libabseil-20211102.0-cxx17_h48a1fff_3
    conda-forge/linux-64::ca-certificates-2022.9.24-ha878542_0
  link_precs:
    conda-forge/linux-64::ca-certificates-2023.7.22-hbcca054_0
    conda-forge/linux-64::hicolor-icon-theme-0.17-ha770c72_2
    conda-forge/linux-64::epoxy-1.5.10-h166bdaf_1
    conda-forge/linux-64::libabseil-20211102.0-cxx17_h48a1fff_2
    conda-forge/linux-64::openssl-1.1.1v-hd590300_0
    conda-forge/linux-64::sigcpp-2.0-2.10.8-h27087fc_0
    conda-forge/linux-64::sparsehash-2.0.4-hcb278e6_1
    conda-forge/linux-64::xorg-recordproto-1.14.2-h7f98852_1002
    conda-forge/linux-64::abseil-cpp-20211102.0-h93e1e8c_2
    conda-forge/linux-64::boost-cpp-1.74.0-h6cacc03_7
    conda-forge/linux-64::libcups-2.3.3-hf5a7f15_1
    conda-forge/noarch::certifi-2023.7.22-pyhd8ed1ab_0
    conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0
    conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0
    conda-forge/linux-64::xorg-libxtst-1.2.3-h7f98852_1002
    conda-forge/linux-64::at-spi2-core-2.40.3-h0630a04_0
    conda-forge/linux-64::boost-1.74.0-py39h5472131_5
    conda-forge/linux-64::cairomm-1.0-1.12.2-h96a316c_4
    conda-forge/linux-64::libgirepository-1.72.0-h26ff761_1
    conda-forge/linux-64::pycairo-1.24.0-py39hc92de75_0
    conda-forge/linux-64::zstandard-0.19.0-py39h6e5214e_2
    conda-forge/linux-64::at-spi2-atk-2.38.0-h0630a04_3
    conda-forge/linux-64::cairomm-1.12.2-ha770c72_4
    conda-forge/linux-64::graph-tool-base-2.45-py39h2fa1a2d_2
    conda-forge/linux-64::pygobject-3.42.1-py39habf54e5_0
    conda-forge/linux-64::gtk3-3.24.33-h13ada96_1
    conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0
    conda-forge/linux-64::graph-tool-2.45-py39h7b6895e_2
    conda-forge/noarch::requests-2.31.0-pyhd8ed1ab_0


## Package Plan ##

  environment location: /opt/conda

  added / updated specs:
    - graph-tool


The following packages will be downloaded:

    package                    |            build
    ---------------------------|-----------------
    abseil-cpp-20211102.0      |       h93e1e8c_2          13 KB  conda-forge
    at-spi2-atk-2.38.0         |       h0630a04_3         332 KB  conda-forge
    at-spi2-core-2.40.3        |       h0630a04_0         643 KB  conda-forge
    boost-1.74.0               |   py39h5472131_5         357 KB  conda-forge
    boost-cpp-1.74.0           |       h6cacc03_7        16.3 MB  conda-forge
    ca-certificates-2023.7.22  |       hbcca054_0         146 KB  conda-forge
    cairomm-1.12.2             |       ha770c72_4          11 KB  conda-forge
    cairomm-1.0-1.12.2         |       h96a316c_4         687 KB  conda-forge
    certifi-2023.7.22          |     pyhd8ed1ab_0         150 KB  conda-forge
    epoxy-1.5.10               |       h166bdaf_1         1.4 MB  conda-forge
    graph-tool-2.45            |   py39h7b6895e_2          27 KB  conda-forge
    graph-tool-base-2.45       |   py39h2fa1a2d_2        68.1 MB  conda-forge
    gtk3-3.24.33               |       h13ada96_1         9.9 MB  conda-forge
    hicolor-icon-theme-0.17    |       ha770c72_2          14 KB  conda-forge
    libabseil-20211102.0       | cxx17_h48a1fff_2         1.1 MB  conda-forge
    libcups-2.3.3              |       hf5a7f15_1         4.6 MB  conda-forge
    libgirepository-1.72.0     |       h26ff761_1         311 KB  conda-forge
    nbclient-0.6.4             |     pyhd8ed1ab_0          65 KB  conda-forge
    openssl-1.1.1v             |       hd590300_0         1.9 MB  conda-forge
    prometheus_client-0.17.1   |     pyhd8ed1ab_0          52 KB  conda-forge
    pycairo-1.24.0             |   py39hc92de75_0         111 KB  conda-forge
    pygobject-3.42.1           |   py39habf54e5_0         290 KB  conda-forge
    pyjwt-2.8.0                |     pyhd8ed1ab_0          24 KB  conda-forge
    requests-2.31.0            |     pyhd8ed1ab_0          55 KB  conda-forge
    sigcpp-2.0-2.10.8          |       h27087fc_0         158 KB  conda-forge
    sparsehash-2.0.4           |       hcb278e6_1          84 KB  conda-forge
    xorg-libxtst-1.2.3         |    h7f98852_1002          31 KB  conda-forge
    xorg-recordproto-1.14.2    |    h7f98852_1002           8 KB  conda-forge
    zstandard-0.19.0           |   py39h6e5214e_2         384 KB  conda-forge
    ------------------------------------------------------------
                                           Total:       107.0 MB

The following NEW packages will be INSTALLED:

  at-spi2-atk        conda-forge/linux-64::at-spi2-atk-2.38.0-h0630a04_3
  at-spi2-core       conda-forge/linux-64::at-spi2-core-2.40.3-h0630a04_0
  boost              conda-forge/linux-64::boost-1.74.0-py39h5472131_5
  boost-cpp          conda-forge/linux-64::boost-cpp-1.74.0-h6cacc03_7
  cairomm            conda-forge/linux-64::cairomm-1.12.2-ha770c72_4
  cairomm-1.0        conda-forge/linux-64::cairomm-1.0-1.12.2-h96a316c_4
  epoxy              conda-forge/linux-64::epoxy-1.5.10-h166bdaf_1
  graph-tool         conda-forge/linux-64::graph-tool-2.45-py39h7b6895e_2
  graph-tool-base    conda-forge/linux-64::graph-tool-base-2.45-py39h2fa1a2d_2
  gtk3               conda-forge/linux-64::gtk3-3.24.33-h13ada96_1
  hicolor-icon-theme conda-forge/linux-64::hicolor-icon-theme-0.17-ha770c72_2
  libcups            conda-forge/linux-64::libcups-2.3.3-hf5a7f15_1
  libgirepository    conda-forge/linux-64::libgirepository-1.72.0-h26ff761_1
  nbclient           conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0
  prometheus_client  conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0
  pycairo            conda-forge/linux-64::pycairo-1.24.0-py39hc92de75_0
  pygobject          conda-forge/linux-64::pygobject-3.42.1-py39habf54e5_0
  pyjwt              conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0
  sigcpp-2.0         conda-forge/linux-64::sigcpp-2.0-2.10.8-h27087fc_0
  sparsehash         conda-forge/linux-64::sparsehash-2.0.4-hcb278e6_1
  xorg-libxtst       conda-forge/linux-64::xorg-libxtst-1.2.3-h7f98852_1002
  xorg-recordproto   conda-forge/linux-64::xorg-recordproto-1.14.2-h7f98852_1002
  zstandard          conda-forge/linux-64::zstandard-0.19.0-py39h6e5214e_2

The following packages will be UPDATED:

  ca-certificates                      2022.9.24-ha878542_0 --> 2023.7.22-hbcca054_0
  certifi                            2022.9.24-pyhd8ed1ab_0 --> 2023.7.22-pyhd8ed1ab_0
  openssl                                 1.1.1s-h166bdaf_0 --> 1.1.1v-hd590300_0
  requests                              2.27.1-pyhd8ed1ab_0 --> 2.31.0-pyhd8ed1ab_0

The following packages will be DOWNGRADED:

  abseil-cpp                          20211102.0-h93e1e8c_3 --> 20211102.0-h93e1e8c_2
  libabseil                     20211102.0-cxx17_h48a1fff_3 --> 20211102.0-cxx17_h48a1fff_2


Preparing transaction: ...working... done
Verifying transaction: ...working... INFO conda.core.link:verify(245): [ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__init__.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/bridge/__init__.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/bridge/graphite.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/context_managers.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/core.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/decorator.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/exposition.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/gc_collector.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/metrics.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/metrics_core.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/mmap_dict.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/multiprocess.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/openmetrics/__init__.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/openmetrics/exposition.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/openmetrics/parser.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/parser.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/platform_collector.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/process_collector.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/registry.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/samples.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/twisted/__init__.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/twisted/_exposition.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/utils.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/values.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/__init__.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/bridge/__pycache__/__init__.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/bridge/__pycache__/graphite.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/context_managers.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/core.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/decorator.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/exposition.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/gc_collector.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/metrics.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/metrics_core.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/mmap_dict.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/multiprocess.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/openmetrics/__pycache__/__init__.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/openmetrics/__pycache__/exposition.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/openmetrics/__pycache__/parser.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/parser.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/platform_collector.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/process_collector.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/registry.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/samples.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/twisted/__pycache__/__init__.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/twisted/__pycache__/_exposition.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/utils.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::prometheus_client-0.17.1-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/prometheus_client/__pycache__/values.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/__init__.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/algorithms.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/api_jws.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/api_jwt.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/exceptions.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/help.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/utils.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/__pycache__/__init__.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/__pycache__/algorithms.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/__pycache__/api_jws.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/__pycache__/api_jwt.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/__pycache__/exceptions.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/__pycache__/help.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::pyjwt-2.8.0-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/jwt/__pycache__/utils.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/linux-64::gtk3-3.24.33-h13ada96_1' cannot be installed due to a
path collision for 'bin/gtk-update-icon-cache'.
This path already exists in the target prefix, and it won't be removed by
an uninstall action in this transaction. The path appears to be coming from
the package 'conda-forge/linux-64::gtk2-2.24.33-h90689f9_2', which is already installed in the prefix.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'bin/jupyter-execute'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/__init__.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/_version.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/cli.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/client.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/exceptions.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/jsonutil.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/output_widget.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/py.typed'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/__init__.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/base.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/conftest.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/fake_kernelmanager.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Autokill.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Check History in Memory.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Clear Output.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Disable Stdin.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Empty Cell.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Error.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Factorials.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/HelloWorld.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Inline Image.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Interrupt.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/JupyterWidgets.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Other Comms.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Output.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Parallel Execute A.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Parallel Execute B.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/SVG.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Skip Exceptions with Cell Tags.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Skip Exceptions.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Skip Execution with Cell Tag.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Sleep1s.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/Unicode.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/UnicodePy3.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/python.png'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/files/update-display-id.ipynb'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/test_client.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/test_util.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/util.py'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/__pycache__/__init__.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/__pycache__/_version.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/__pycache__/cli.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/__pycache__/client.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/__pycache__/exceptions.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/__pycache__/jsonutil.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/__pycache__/output_widget.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/__pycache__/__init__.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/__pycache__/base.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/__pycache__/conftest.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/__pycache__/fake_kernelmanager.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/__pycache__/test_client.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/tests/__pycache__/test_util.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

, ClobberError: The package 'conda-forge/noarch::nbclient-0.6.4-pyhd8ed1ab_0' cannot be installed due to a
path collision for 'lib/python3.9/site-packages/nbclient/__pycache__/util.cpython-39.pyc'.
This path already exists in the target prefix, and it won't be removed
by an uninstall action in this transaction. The path is one that conda
doesn't recognize. It may have been created by another package manager.

]
done
Executing transaction: ...working... INFO conda.core.link:_execute_actions(766): ===> UNLINKING PACKAGE: conda-forge/noarch::requests-2.27.1-pyhd8ed1ab_0 <===
  prefix=/opt/conda

INFO conda.core.link:_execute_actions(766): ===> UNLINKING PACKAGE: conda-forge/noarch::certifi-2022.9.24-pyhd8ed1ab_0 <===
  prefix=/opt/conda

INFO conda.core.link:_execute_actions(766): ===> UNLINKING PACKAGE: conda-forge/linux-64::abseil-cpp-20211102.0-h93e1e8c_3 <===
  prefix=/opt/conda

INFO conda.core.link:_execute_actions(766): ===> UNLINKING PACKAGE: conda-forge/linux-64::openssl-1.1.1s-h166bdaf_0 <===
  prefix=/opt/conda

INFO conda.core.link:_execute_actions(766): ===> UNLINKING PACKAGE: conda-forge/linux-64::libabseil-20211102.0-cxx17_h48a1fff_3 <===
  prefix=/opt/conda

INFO conda.core.link:_execute_actions(766): ===> UNLINKING PACKAGE: conda-forge/linux-64::ca-certificates-2022.9.24-ha878542_0 <===
  prefix=/opt/conda

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::ca-certificates-2023.7.22-hbcca054_0 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/ca-certificates-2023.7.22-hbcca054_0

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::hicolor-icon-theme-0.17-ha770c72_2 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/hicolor-icon-theme-0.17-ha770c72_2

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::epoxy-1.5.10-h166bdaf_1 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/epoxy-1.5.10-h166bdaf_1

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::libabseil-20211102.0-cxx17_h48a1fff_2 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/libabseil-20211102.0-cxx17_h48a1fff_2

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::openssl-1.1.1v-hd590300_0 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/openssl-1.1.1v-hd590300_0

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::sigcpp-2.0-2.10.8-h27087fc_0 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/sigcpp-2.0-2.10.8-h27087fc_0

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::sparsehash-2.0.4-hcb278e6_1 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/sparsehash-2.0.4-hcb278e6_1

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::xorg-recordproto-1.14.2-h7f98852_1002 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/xorg-recordproto-1.14.2-h7f98852_1002

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::abseil-cpp-20211102.0-h93e1e8c_2 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/abseil-cpp-20211102.0-h93e1e8c_2

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::boost-cpp-1.74.0-h6cacc03_7 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/boost-cpp-1.74.0-h6cacc03_7

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::libcups-2.3.3-hf5a7f15_1 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/libcups-2.3.3-hf5a7f15_1

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::certifi-2023.7.22-pyhd8ed1ab_0 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/certifi-2023.7.22-pyhd8ed1ab_0

INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::prometheus_client-0.17.1-pyhd8ed1ab_0 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/prometheus_client-0.17.1-pyhd8ed1ab_0

INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/__init__.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/bridge/__init__.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/bridge/graphite.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/context_managers.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/core.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/decorator.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/exposition.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/gc_collector.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/metrics.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/metrics_core.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/mmap_dict.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/multiprocess.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/openmetrics/__init__.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/openmetrics/exposition.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/openmetrics/parser.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/parser.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/platform_collector.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/process_collector.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/registry.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/samples.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/twisted/__init__.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/twisted/_exposition.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/utils.py'
INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/prometheus_client/values.py'
INFO conda.core.link:_execute_actions(771): ===> LINKING PACKAGE: conda-forge::pyjwt-2.8.0-pyhd8ed1ab_0 <===
  prefix=/opt/conda
  source=/opt/conda/pkgs/pyjwt-2.8.0-pyhd8ed1ab_0

INFO conda.gateways.disk.create:create_link(353): file exists, but clobbering: '/opt/conda/lib/python3.9/site-packages/jwt/__init__.py'
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done
*** finish!!!
Requirement already satisfied: scipy in /opt/conda/lib/python3.9/site-packages (1.7.3)
Collecting scipy
  Using cached scipy-1.11.2-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (36.5 MB)
Requirement already satisfied: networkx in /opt/conda/lib/python3.9/site-packages (2.8.7)
Collecting networkx
  Using cached networkx-3.1-py3-none-any.whl (2.1 MB)
Requirement already satisfied: numpy<1.28.0,>=1.21.6 in /opt/conda/lib/python3.9/site-packages (from scipy) (1.21.6)
Installing collected packages: scipy, networkx
  Attempting uninstall: scipy
    Found existing installation: scipy 1.7.3
    Uninstalling scipy-1.7.3:
      Successfully uninstalled scipy-1.7.3
  Attempting uninstall: networkx
    Found existing installation: networkx 2.8.7
    Uninstalling networkx-2.8.7:
      Successfully uninstalled networkx-2.8.7
ERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.
pointpats 2.2.0 requires opencv-contrib-python>=4.2.0, which is not installed.
pymc3 3.11.5 requires scipy<1.8.0,>=1.7.3, but you have scipy 1.11.2 which is incompatible.
Successfully installed networkx-3.1 scipy-1.11.2
networkx: 3.1
graph-tool: 2.45 (commit 71a3b6d2, )

Test Graph-tool and Networkx¶

In [2]:
g_gt = gt.Graph(directed=True)

v_A = g_gt.add_vertex()
v_B = g_gt.add_vertex()
v_C = g_gt.add_vertex()
v_D = g_gt.add_vertex()
v_E = g_gt.add_vertex()
v_F = g_gt.add_vertex()
g_gt.vp.name = g_gt.new_vertex_property("string")
g_gt.vp.name[v_A] = "A"
g_gt.vp.name[v_B] = "B"
g_gt.vp.name[v_C] = "C"
g_gt.vp.name[v_D] = "D"
g_gt.vp.name[v_E] = "E"
g_gt.vp.name[v_F] = "F"

e_BA = g_gt.add_edge(v_B, v_A)
e_CA = g_gt.add_edge(v_C, v_A)
e_BC = g_gt.add_edge(v_B, v_C)
e_ED = g_gt.add_edge(v_E, v_D)
e_FD = g_gt.add_edge(v_F, v_D)
e_EF = g_gt.add_edge(v_E, v_F)
e_AD = g_gt.add_edge(v_A, v_D)
g_gt.ep.weight = g_gt.new_edge_property("double")
g_gt.ep.weight[e_BA] = 10
g_gt.ep.weight[e_CA] = 20
g_gt.ep.weight[e_BC] = 30
g_gt.ep.weight[e_ED] = 10
g_gt.ep.weight[e_FD] = 20
g_gt.ep.weight[e_EF] = 30
g_gt.ep.weight[e_AD] = 100

deg = g_gt.degree_property_map('in')
deg.a = 30*deg.a
gt.graph_draw(g_gt,
              vertex_text = g_gt.properties[('v', 'name')], vertex_size=deg,
              edge_text = g_gt.properties[('e', 'weight')])
Out[2]:
<VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc85dfc9700, at 0x7fc85dfce520>
In [3]:
g_nx = nx.DiGraph()
g_nx.add_weighted_edges_from([('B', 'A', 10), ('C', 'A', 20), ('B', 'C', 30),
                   ('E', 'D', 10), ('F', 'D', 20), ('E', 'F', 30),
                   ('A', 'D', 100)])
nx.draw(g_nx, with_labels=True)
In [4]:
print(nx.is_directed(g_nx))
print(nx.is_weighted(g_nx))
print(nx.number_of_nodes(g_nx))
print(nx.number_of_edges(g_nx))
print(nx.density(g_nx))
print(g_nx.in_degree('A'))
print(g_nx.out_degree('A'))
print(g_nx.degree('A'))
print(g_nx.in_degree('A', weight='weight'))
print(g_nx.out_degree('A', weight='weight'))
print(g_nx.degree('A', weight='weight'))
print(nx.is_weakly_connected(g_nx))
print(nx.is_strongly_connected(g_nx))
print(nx.average_shortest_path_length(g_nx.to_undirected(), weight='weight'))
def nx_diameter_with_weight(G, weight_str):
    diameters = []
    for node in G.nodes():
        shortest_paths = nx.single_source_dijkstra(G, source=node, weight=weight_str)[0]
        max_shortest_path = max(shortest_paths.values())
        diameters.append(max_shortest_path)
    return max(diameters)
print(nx_diameter_with_weight(g_nx.to_undirected(), 'weight'))
print(nx.clustering(g_nx, 'A'))

True
True
6
7
0.23333333333333334
2
1
3
30
100
130
True
False
80.0
140
0.16666666666666666
In [5]:
# SBMs
g_gt = gt.collection.data["football"]
state = gt.minimize_blockmodel_dl(g_gt)
state.draw(pos=g_gt.vp.pos)

b = gt.contiguous_map(state.get_blocks())
state = state.copy(b=b)
e = state.get_matrix()
B = state.get_nonempty_B()
plt.matshow(e.todense()[:B, :B], cmap='viridis')
plt.xlabel('Group r')
plt.ylabel('Group s')
plt.colorbar()
plt.show()

Data¶

Import FNA Data¶

In [6]:
## data
zip_path = 'FNA network.zip'
dir = 'FNA network'
if not os.path.exists(dir):
    print('*** unzip data.zip')
    with zp.ZipFile(zip_path) as arc:
        arc.extractall()

file_list = os.listdir(dir)
file_list.sort()

print(len(file_list))
file_list

27
Out[6]:
['20150331.csv',
 '20150630.csv',
 '20150930.csv',
 '20151231.csv',
 '20160331.csv',
 '20160630.csv',
 '20160930.csv',
 '20161231.csv',
 '20170331.csv',
 '20170630.csv',
 '20170930.csv',
 '20171231.csv',
 '20180331.csv',
 '20180630.csv',
 '20180930.csv',
 '20181231.csv',
 '20190331.csv',
 '20190630.csv',
 '20190930.csv',
 '20191231.csv',
 '20200331.csv',
 '20200630.csv',
 '20200930.csv',
 '20201231.csv',
 '20210331.csv',
 '20210630.csv',
 '20210930.csv']
In [7]:
time_list = []
for file_name in file_list:
    time_list.append(file_name.replace('.csv',''))

Data Inspect¶

In [8]:
# pd_inspect
pd_inspect = pd.read_csv(dir + '/' + file_list[0])

print(pd_inspect.shape)
print(pd_inspect.columns)
pd_inspect.head()

(406, 21)
Index(['net_id', 'arc_id', 'from_id', 'to_id', 'borrower', 'claims_held',
       'claims_held_10_change', 'claims_held_10_change_max',
       'claims_held_10_change_min', 'claims_held_2_change',
       'claims_held_2_change_max', 'claims_held_2_change_min',
       'claims_held_5_change', 'claims_held_5_change_max',
       'claims_held_5_change_min', 'claims_held_max', 'claims_held_min',
       'lender', 'share_of_claims_held', 'share_of_claims_held_max',
       'share_of_claims_held_min'],
      dtype='object')
Out[8]:
net_id arc_id from_id to_id borrower claims_held claims_held_10_change claims_held_10_change_max claims_held_10_change_min claims_held_2_change ... claims_held_2_change_min claims_held_5_change claims_held_5_change_max claims_held_5_change_min claims_held_max claims_held_min lender share_of_claims_held share_of_claims_held_max share_of_claims_held_min
0 2015/3/31 AT-AU-0 AT AU Austria 5.220850e+08 NaN NaN NaN 63385000.0 ... -1.244000e+09 -1.586615e+09 6.050000e+08 -2.894000e+09 3.436000e+09 4.450000e+08 Australia 0.005037 0.014129 0.003330
1 2015/3/31 AT-BE-0 AT BE Austria 1.750940e+09 NaN NaN NaN 87716000.0 ... -3.459000e+09 -1.177284e+09 1.641000e+09 -3.771637e+09 6.063000e+09 1.550000e+09 Belgium 0.016893 0.029052 0.011835
2 2015/3/31 AT-CA-0 AT CA Austria 8.363850e+08 NaN NaN NaN -122939000.0 ... -6.610000e+08 -8.139390e+08 8.910000e+08 -1.297000e+09 2.204000e+09 7.510000e+08 Canada 0.008069 0.010148 0.005185
3 2015/3/31 AT-CH-0 AT CH Austria 6.733410e+09 NaN NaN NaN 551087000.0 ... -6.296000e+09 -6.938913e+09 6.476000e+09 -6.387000e+09 1.312600e+10 5.288694e+09 Switzerland 0.064963 0.081206 0.037446
4 2015/3/31 AT-CL-0 AT CL Austria 1.416100e+07 NaN NaN NaN -7430000.0 ... -1.780000e+08 -4.543000e+07 3.300000e+07 -1.740000e+08 2.390000e+08 7.000000e+06 Chile 0.000137 0.001536 0.000051

5 rows × 21 columns

In [9]:
print("borrower: len=" + str(len(pd_inspect['borrower'].unique())) +
                             ", array=" + np.array2string(pd_inspect['borrower'].unique()))
print("lender: len=" + str(len(pd_inspect['lender'].unique())) +
                              ", array=" + np.array2string(pd_inspect['lender'].unique()))
print("arc_id: len=" + str(len(pd_inspect['arc_id'].unique())))

borrower: len=21, array=['Austria' 'Australia' 'Belgium' 'Canada' 'Switzerland' 'Chile' 'Germany'
 'Spain' 'Finland' 'France' 'United_Kingdom' 'Greece' 'Ireland' 'Italy'
 'Japan' 'South_Korea' 'Netherlands' 'Portugal' 'Sweden' 'Turkey'
 'United_States']
lender: len=22, array=['Australia' 'Belgium' 'Canada' 'Switzerland' 'Chile' 'Germany' 'Spain'
 'Finland' 'France' 'United_Kingdom' 'Greece' 'Ireland' 'India' 'Italy'
 'Japan' 'South_Korea' 'Netherlands' 'Portugal' 'Sweden' 'Turkey'
 'United_States' 'Austria']
arc_id: len=406
In [10]:
# pd_list: we only consider claims_held/USD
columns_key = ['arc_id','from_id','to_id','borrower','lender']
pd_claims_held_dict = {}
for one_time in time_list:
    pd_claims_held_dict[one_time] = pd.read_csv(dir + '/' + one_time + '.csv')[columns_key + ['claims_held']]

print(pd_claims_held_dict[time_list[0]].shape)
pd_claims_held_dict[time_list[0]].head()

(406, 6)
Out[10]:
arc_id from_id to_id borrower lender claims_held
0 AT-AU-0 AT AU Austria Australia 5.220850e+08
1 AT-BE-0 AT BE Austria Belgium 1.750940e+09
2 AT-CA-0 AT CA Austria Canada 8.363850e+08
3 AT-CH-0 AT CH Austria Switzerland 6.733410e+09
4 AT-CL-0 AT CL Austria Chile 1.416100e+07
In [11]:
# pd_merge
pd_claims_held_merge = pd_claims_held_dict[time_list[0]].rename(columns={'claims_held':time_list[0]})
for i in range(1, len(time_list)):
    pd_claims_held_merge = pd_claims_held_merge.merge(
      pd_claims_held_dict[time_list[i]].rename(columns={'claims_held':time_list[i]}), how='outer', on=columns_key)

print(pd_claims_held_merge.shape)
pd_claims_held_merge.head()

(417, 32)
Out[11]:
arc_id from_id to_id borrower lender 20150331 20150630 20150930 20151231 20160331 ... 20190630 20190930 20191231 20200331 20200630 20200930 20201231 20210331 20210630 20210930
0 AT-AU-0 AT AU Austria Australia 5.220850e+08 5.084990e+08 4.856030e+08 4.644340e+08 5.175790e+08 ... 7.276380e+08 7.059820e+08 6.804890e+08 6.906940e+08 8.673920e+08 7.464550e+08 7.066430e+08 5.567450e+08 5.362950e+08 4.686770e+08
1 AT-BE-0 AT BE Austria Belgium 1.750940e+09 1.849885e+09 1.628480e+09 1.658547e+09 1.913879e+09 ... 1.779613e+09 2.025959e+09 2.038951e+09 2.471685e+09 2.676054e+09 2.576757e+09 2.456031e+09 2.479068e+09 2.659388e+09 2.712196e+09
2 AT-CA-0 AT CA Austria Canada 8.363850e+08 7.752660e+08 8.305000e+08 7.912120e+08 1.103028e+09 ... 1.371020e+09 1.261644e+09 1.325207e+09 1.526138e+09 1.733183e+09 1.750037e+09 1.841479e+09 1.791729e+09 2.011624e+09 1.983479e+09
3 AT-CH-0 AT CH Austria Switzerland 6.733410e+09 6.627628e+09 6.614905e+09 5.406037e+09 6.069540e+09 ... 1.341007e+10 1.141622e+10 8.002445e+09 1.069121e+10 9.524585e+09 9.707074e+09 9.208257e+09 9.387236e+09 8.534151e+09 8.151934e+09
4 AT-CL-0 AT CL Austria Chile 1.416100e+07 1.679800e+07 1.669500e+07 2.351900e+07 2.146300e+07 ... 2.170100e+07 2.030500e+07 7.084000e+07 7.724400e+07 3.058500e+07 1.125200e+08 4.499800e+07 4.861500e+07 8.117600e+07 7.893600e+07

5 rows × 32 columns

In [12]:
print("borrower: len=" + str(len(pd_claims_held_merge['borrower'].unique())) +
                             ", array=" + np.array2string(pd_claims_held_merge['borrower'].unique()))
print("lender: len=" + str(len(pd_claims_held_merge['lender'].unique())) +
                              ", array=" + np.array2string(pd_claims_held_merge['lender'].unique()))
print("arc_id: len=" + str(len(pd_claims_held_merge['arc_id'].unique())))

borrower: len=21, array=['Austria' 'Australia' 'Belgium' 'Canada' 'Switzerland' 'Chile' 'Germany'
 'Spain' 'Finland' 'France' 'United_Kingdom' 'Greece' 'Ireland' 'Italy'
 'Japan' 'South_Korea' 'Netherlands' 'Portugal' 'Sweden' 'Turkey'
 'United_States']
lender: len=22, array=['Australia' 'Belgium' 'Canada' 'Switzerland' 'Chile' 'Germany' 'Spain'
 'Finland' 'France' 'United_Kingdom' 'Greece' 'Ireland' 'India' 'Italy'
 'Japan' 'South_Korea' 'Netherlands' 'Portugal' 'Sweden' 'Turkey'
 'United_States' 'Austria']
arc_id: len=417
In [13]:
pd_claims_held_merge.describe()
Out[13]:
20150331 20150630 20150930 20151231 20160331 20160630 20160930 20161231 20170331 20170630 ... 20190630 20190930 20191231 20200331 20200630 20200930 20201231 20210331 20210630 20210930
count 4.060000e+02 4.040000e+02 4.020000e+02 4.000000e+02 4.030000e+02 4.030000e+02 4.000000e+02 4.020000e+02 3.990000e+02 4.000000e+02 ... 4.040000e+02 4.080000e+02 4.060000e+02 4.090000e+02 4.080000e+02 4.060000e+02 4.080000e+02 4.050000e+02 4.070000e+02 4.070000e+02
mean 3.896289e+10 3.901076e+10 3.891243e+10 3.747723e+10 3.899392e+10 3.907801e+10 3.890906e+10 3.724084e+10 3.936975e+10 4.033251e+10 ... 4.290681e+10 4.239769e+10 4.212174e+10 4.559877e+10 4.526763e+10 4.642467e+10 4.743614e+10 4.938093e+10 4.875622e+10 4.882246e+10
std 1.150953e+11 1.145297e+11 1.137052e+11 1.122800e+11 1.170230e+11 1.190124e+11 1.191671e+11 1.171589e+11 1.217479e+11 1.220391e+11 ... 1.347591e+11 1.366200e+11 1.376339e+11 1.541051e+11 1.467481e+11 1.483425e+11 1.516806e+11 1.610586e+11 1.576152e+11 1.614671e+11
min 3.400000e+04 3.500000e+04 1.700000e+04 1.600000e+04 2.400000e+04 3.000000e+03 1.900000e+04 2.000000e+03 2.000000e+03 1.600000e+04 ... 3.200000e+04 1.000000e+03 6.000000e+03 5.000000e+03 2.000000e+03 2.500000e+04 2.000000e+03 2.000000e+03 8.000000e+03 4.000000e+03
25% 4.332500e+08 4.781960e+08 5.032530e+08 5.098255e+08 4.971165e+08 4.590000e+08 5.229000e+08 4.096500e+08 4.568110e+08 4.260468e+08 ... 4.666802e+08 4.887218e+08 6.085820e+08 4.748340e+08 4.935000e+08 5.412948e+08 5.079855e+08 5.163610e+08 6.380995e+08 5.060000e+08
50% 3.905123e+09 4.170236e+09 4.025781e+09 4.016555e+09 4.500000e+09 4.102000e+09 4.315762e+09 3.635000e+09 4.241088e+09 4.421241e+09 ... 5.037840e+09 5.039014e+09 5.142062e+09 5.083272e+09 4.759000e+09 5.074405e+09 4.720122e+09 4.948706e+09 5.030000e+09 4.564000e+09
75% 2.505605e+10 2.512682e+10 2.536450e+10 2.596236e+10 2.553878e+10 2.469195e+10 2.536008e+10 2.487500e+10 2.704789e+10 2.822338e+10 ... 2.934108e+10 2.797351e+10 2.761575e+10 2.877100e+10 2.916425e+10 3.123221e+10 3.055900e+10 3.444372e+10 3.307950e+10 3.294450e+10
max 1.402600e+12 1.367110e+12 1.419200e+12 1.480200e+12 1.562440e+12 1.574080e+12 1.632530e+12 1.621990e+12 1.664630e+12 1.602110e+12 ... 1.720280e+12 1.782080e+12 1.814070e+12 2.083960e+12 1.929570e+12 1.928240e+12 1.970800e+12 2.139220e+12 2.004560e+12 2.062660e+12

8 rows × 27 columns

In [14]:
# we mainly consider mean, 50% and max in a time line
describe_focus = ['mean','50%','max']
pd_claims_held_merge_describe = pd_claims_held_merge.describe().T

fig, axs = plt.subplots(len(describe_focus),figsize=(7,6))

for i in range(0, len(describe_focus)):
    axs[i].plot(pd_claims_held_merge_describe[describe_focus[i]], label=describe_focus[i])
    axs[i].set_title(describe_focus[i])
    axs[i].xaxis.set_tick_params(rotation=45)
    axs[i].legend()

plt.tight_layout()
plt.show()

Network Generation and Inspect¶

  • To be convient, the unit for weight|claims_held is $10^9$ USD (billion)
  • Mainly use networkx
  • arrow: from-lender & to: borrower

Network Generation¶

In [15]:
graphml_dir = 'FNA graphml'
if not os.path.exists(graphml_dir):
    print('*** generate graphml')
    os.makedirs(graphml_dir)
    for one_time in time_list:
        pd_claims_held_dict[one_time]['claims_held']/=10**9
        G = nx.from_pandas_edgelist(
            pd_claims_held_dict[one_time],
            source = 'lender', target = 'borrower',
            edge_attr='claims_held', create_using=nx.DiGraph())
        # add reciprocal
        for src, tar, wgt in G.edges.data('claims_held'):
            G.edges[src, tar]['claims_held_reciprocal'] = 1 / wgt
        nx.write_graphml_lxml(G, graphml_dir + "/" + one_time + ".graphml")

print("*** read graphml for nx")
G_nxs = {}
for one_time in time_list:
    G = nx.read_graphml(graphml_dir + "/" + one_time + ".graphml")
    print("nx time: " + one_time + ", nodes: " + str(G.number_of_nodes()) + ", edges: " + str(G.number_of_edges()))
    G_nxs[one_time] = G

print("*** read graphml for gt")
G_gts = {}
for one_time in time_list:
    G = gt.load_graph(graphml_dir + "/" + one_time + ".graphml")
    print("gt time: " + one_time + ", nodes: " + str(G.num_vertices()) + ", edges: " + str(G.num_edges()))
    G_gts[one_time] = G

*** read graphml for nx
nx time: 20150331, nodes: 22, edges: 406
nx time: 20150630, nodes: 22, edges: 404
nx time: 20150930, nodes: 22, edges: 402
nx time: 20151231, nodes: 22, edges: 400
nx time: 20160331, nodes: 22, edges: 403
nx time: 20160630, nodes: 22, edges: 403
nx time: 20160930, nodes: 22, edges: 400
nx time: 20161231, nodes: 22, edges: 402
nx time: 20170331, nodes: 22, edges: 399
nx time: 20170630, nodes: 22, edges: 400
nx time: 20170930, nodes: 22, edges: 401
nx time: 20171231, nodes: 22, edges: 402
nx time: 20180331, nodes: 22, edges: 401
nx time: 20180630, nodes: 22, edges: 403
nx time: 20180930, nodes: 22, edges: 405
nx time: 20181231, nodes: 22, edges: 402
nx time: 20190331, nodes: 22, edges: 407
nx time: 20190630, nodes: 22, edges: 404
nx time: 20190930, nodes: 22, edges: 408
nx time: 20191231, nodes: 22, edges: 406
nx time: 20200331, nodes: 22, edges: 409
nx time: 20200630, nodes: 22, edges: 408
nx time: 20200930, nodes: 22, edges: 406
nx time: 20201231, nodes: 22, edges: 408
nx time: 20210331, nodes: 22, edges: 405
nx time: 20210630, nodes: 22, edges: 407
nx time: 20210930, nodes: 22, edges: 407
*** read graphml for gt
gt time: 20150331, nodes: 22, edges: 406
gt time: 20150630, nodes: 22, edges: 404
gt time: 20150930, nodes: 22, edges: 402
gt time: 20151231, nodes: 22, edges: 400
gt time: 20160331, nodes: 22, edges: 403
gt time: 20160630, nodes: 22, edges: 403
gt time: 20160930, nodes: 22, edges: 400
gt time: 20161231, nodes: 22, edges: 402
gt time: 20170331, nodes: 22, edges: 399
gt time: 20170630, nodes: 22, edges: 400
gt time: 20170930, nodes: 22, edges: 401
gt time: 20171231, nodes: 22, edges: 402
gt time: 20180331, nodes: 22, edges: 401
gt time: 20180630, nodes: 22, edges: 403
gt time: 20180930, nodes: 22, edges: 405
gt time: 20181231, nodes: 22, edges: 402
gt time: 20190331, nodes: 22, edges: 407
gt time: 20190630, nodes: 22, edges: 404
gt time: 20190930, nodes: 22, edges: 408
gt time: 20191231, nodes: 22, edges: 406
gt time: 20200331, nodes: 22, edges: 409
gt time: 20200630, nodes: 22, edges: 408
gt time: 20200930, nodes: 22, edges: 406
gt time: 20201231, nodes: 22, edges: 408
gt time: 20210331, nodes: 22, edges: 405
gt time: 20210630, nodes: 22, edges: 407
gt time: 20210930, nodes: 22, edges: 407

Network inspect¶

In [16]:
G_temp = G_nxs[time_list[0]]
# pos = nx.circular_layout(G_filt),
nx.draw(G_temp, with_labels=True,
        node_color='#8b0000', node_size=700,
        font_size=6, font_color='white', font_family='serif', font_weight='light',
        arrowsize=5, edge_color='black', width=1)
In [17]:
print(nx.is_strongly_connected(G_temp))
print(nx.is_weakly_connected(G_temp))

False
True
In [18]:
nx.number_strongly_connected_components(G_temp)
Out[18]:
2
In [19]:
components = nx.strongly_connected_components(G_temp)
for c in components:
    print(c)

{'Austria', 'United_Kingdom', 'Switzerland', 'South_Korea', 'Germany', 'Sweden', 'Chile', 'Spain', 'Portugal', 'Japan', 'Canada', 'Finland', 'Turkey', 'Australia', 'United_States', 'Ireland', 'Italy', 'France', 'Belgium', 'Greece', 'Netherlands'}
{'India'}

Inspect with Basic and Homogeneous Graph Statistics¶

In [20]:
G_nxs_statistics = {}
for name,G_nx in G_nxs.items():
    print("*** process ",name)
    statistics = {}
    # Number of nodes
    statistics['nodes'] = nx.number_of_nodes(G_nx)
    # Number of links
    statistics['links'] = nx.number_of_edges(G_nx)
    # Density
    statistics['density'] = nx.density(G_nx)
    # Average degrees (in-degree, out-degree, total degree)
    statistics['avg_in_degree'] = sum([x[1] for x in G_nx.in_degree()])/statistics['nodes']
    statistics['avg_out_degree'] = sum([x[1] for x in G_nx.out_degree()])/statistics['nodes']
    statistics['avg_total_degree'] = sum([x[1] for x in G_nx.degree()])/statistics['nodes']
    # Average strength (in-strength, out-strength, total strength)
    statistics['avg_in_strength'] = sum([x[1] for x in G_nx.in_degree(weight='claims_held')])/statistics['nodes']
    statistics['avg_out_strength'] = sum([x[1] for x in G_nx.out_degree(weight='claims_held')])/statistics['nodes']
    statistics['avg_total_strength'] = sum([x[1] for x in G_nx.degree(weight='claims_held')])/statistics['nodes']
    # Maximum strength (in-strength, out-strength, total strength)
    statistics['max_in_strength'] = max([x[1] for x in G_nx.in_degree(weight='claims_held')])
    statistics['max_out_strength'] = max([x[1] for x in G_nx.out_degree(weight='claims_held')])
    statistics['max_total_strength'] = max([x[1] for x in G_nx.degree(weight='claims_held')])
    # Average clustering coefficient
    statistics['avg_clus_coef'] = nx.average_clustering(G_nx)
    statistics['avg_clus_coef_weight'] = nx.average_clustering(G_nx, weight="claims_held")
    # Average path length for G_strong
    components = nx.strongly_connected_components(G_nx) # Identify all components.
    G_strong = nx.subgraph(G_nx, max(components, key = len)) # Subgraph the largest componenet.
    statistics['avg_path_length_for_strong'] = nx.average_shortest_path_length(G_strong)
    statistics['avg_path_length_weight_for_strong'] = nx.average_shortest_path_length(G_strong, weight='claims_held')
    # Diameter
    statistics['diameter_for_strong'] = nx.diameter(G_strong)
    statistics['diameter_weight_for_strong'] = nx_diameter_with_weight(G_strong, weight_str='claims_held')

    G_nxs_statistics[name] = statistics
print("finish")

*** process  20150331
*** process  20150630
*** process  20150930
*** process  20151231
*** process  20160331
*** process  20160630
*** process  20160930
*** process  20161231
*** process  20170331
*** process  20170630
*** process  20170930
*** process  20171231
*** process  20180331
*** process  20180630
*** process  20180930
*** process  20181231
*** process  20190331
*** process  20190630
*** process  20190930
*** process  20191231
*** process  20200331
*** process  20200630
*** process  20200930
*** process  20201231
*** process  20210331
*** process  20210630
*** process  20210930
finish
In [21]:
pd.DataFrame.from_dict(G_nxs_statistics, orient='index').T
Out[21]:
20150331 20150630 20150930 20151231 20160331 20160630 20160930 20161231 20170331 20170630 ... 20190630 20190930 20191231 20200331 20200630 20200930 20201231 20210331 20210630 20210930
nodes 22.000000 22.000000 22.000000 22.000000 22.000000 22.000000 22.000000 22.000000 22.000000 22.000000 ... 22.000000 22.000000 22.000000 22.000000 22.000000 22.000000 22.000000 22.000000 22.000000 22.000000
links 406.000000 404.000000 402.000000 400.000000 403.000000 403.000000 400.000000 402.000000 399.000000 400.000000 ... 404.000000 408.000000 406.000000 409.000000 408.000000 406.000000 408.000000 405.000000 407.000000 407.000000
density 0.878788 0.874459 0.870130 0.865801 0.872294 0.872294 0.865801 0.870130 0.863636 0.865801 ... 0.874459 0.883117 0.878788 0.885281 0.883117 0.878788 0.883117 0.876623 0.880952 0.880952
avg_in_degree 18.454545 18.363636 18.272727 18.181818 18.318182 18.318182 18.181818 18.272727 18.136364 18.181818 ... 18.363636 18.545455 18.454545 18.590909 18.545455 18.454545 18.545455 18.409091 18.500000 18.500000
avg_out_degree 18.454545 18.363636 18.272727 18.181818 18.318182 18.318182 18.181818 18.272727 18.136364 18.181818 ... 18.363636 18.545455 18.454545 18.590909 18.545455 18.454545 18.545455 18.409091 18.500000 18.500000
avg_total_degree 36.909091 36.727273 36.545455 36.363636 36.636364 36.636364 36.363636 36.545455 36.272727 36.363636 ... 36.727273 37.090909 36.909091 37.181818 37.090909 36.909091 37.090909 36.818182 37.000000 37.000000
avg_in_strength 719.042366 716.379387 711.036157 681.404122 714.297744 715.838051 707.437403 680.491755 714.024134 733.318375 ... 787.925090 786.284425 777.337604 847.722596 839.508807 856.746106 879.724690 909.058090 901.990000 903.215459
avg_out_strength 719.042366 716.379387 711.036157 681.404122 714.297744 715.838051 707.437403 680.491755 714.024134 733.318375 ... 787.925090 786.284425 777.337604 847.722596 839.508807 856.746106 879.724689 909.058090 901.990000 903.215459
avg_total_strength 1438.084732 1432.758773 1422.072315 1362.808243 1428.595488 1431.676103 1414.874806 1360.983510 1428.048267 1466.636749 ... 1575.850179 1572.568851 1554.675208 1695.445192 1679.017615 1713.492211 1759.449379 1818.116180 1803.980001 1806.430918
max_in_strength 2381.115900 2326.251300 2390.292600 2467.546100 2601.884100 2620.705300 2683.908000 2648.925800 2681.878700 2647.471400 ... 2896.305200 2945.025900 2992.358400 3229.681000 3112.945500 3158.931800 3285.426100 3437.434000 3277.325700 3307.011700
max_out_strength 5460.318715 5420.730515 5316.256447 5164.569164 5398.290632 5509.303256 5381.162725 5346.196242 5577.909380 5626.202025 ... 6177.127795 6272.336411 6290.562397 7169.467488 6719.901182 6733.283824 6803.039060 7217.514632 7029.859086 7294.908210
max_total_strength 7426.806715 7377.435515 7217.589447 6936.898164 7266.095632 7415.743256 7282.842725 7236.680242 7521.092380 7601.813025 ... 8315.813795 8396.423411 8260.562397 9463.306488 9020.535182 9029.639824 9131.186060 9818.741632 9664.494086 9908.429210
avg_clus_coef 0.918406 0.917345 0.912777 0.910329 0.915476 0.921938 0.915274 0.916467 0.913212 0.911958 ... 0.919148 0.920662 0.919822 0.922576 0.920903 0.920680 0.920628 0.921047 0.921228 0.922612
avg_clus_coef_weight 0.011140 0.011400 0.010927 0.010065 0.009951 0.009839 0.009490 0.008984 0.009305 0.009843 ... 0.009956 0.009522 0.009292 0.008604 0.009292 0.009548 0.009491 0.009025 0.009543 0.009153
avg_path_length_for_strong 1.073810 1.076190 1.080952 1.085714 1.078571 1.073810 1.080952 1.078571 1.083333 1.083333 ... 1.076190 1.069048 1.071429 1.066667 1.069048 1.071429 1.069048 1.071429 1.069048 1.069048
avg_path_length_weight_for_strong 1.460431 1.348494 1.326041 1.277487 1.257172 1.173444 1.268087 1.149238 1.264553 1.354689 ... 1.310787 1.329745 1.384722 1.525382 1.367426 1.276627 1.246829 1.307801 1.337465 1.360774
diameter_for_strong 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 ... 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000
diameter_weight_for_strong 16.712108 15.222612 15.507221 12.604031 11.869555 12.290150 11.677985 10.409927 11.661216 13.087702 ... 11.249915 10.524969 11.125905 12.981584 12.800612 13.101806 12.418850 12.693274 12.703218 14.041476

18 rows × 27 columns

In [22]:
pd.DataFrame.from_dict(G_nxs_statistics, orient='index').describe().T
Out[22]:
count mean std min 25% 50% 75% max
nodes 27.0 22.000000 0.000000 22.000000 22.000000 22.000000 22.000000 22.000000
links 27.0 404.000000 2.935198 399.000000 402.000000 404.000000 406.500000 409.000000
density 27.0 0.874459 0.006353 0.863636 0.870130 0.874459 0.879870 0.885281
avg_in_degree 27.0 18.363636 0.133418 18.136364 18.272727 18.363636 18.477273 18.590909
avg_out_degree 27.0 18.363636 0.133418 18.136364 18.272727 18.363636 18.477273 18.590909
avg_total_degree 27.0 36.727273 0.266836 36.272727 36.545455 36.727273 36.954545 37.181818
avg_in_strength 27.0 775.640146 69.507916 680.491755 716.108719 766.387224 814.280785 909.058090
avg_out_strength 27.0 775.640146 69.507916 680.491755 716.108719 766.387224 814.280785 909.058090
avg_total_strength 27.0 1551.280292 139.015833 1360.983510 1432.217438 1532.774448 1628.561570 1818.116180
max_in_strength 27.0 2837.377944 308.274066 2326.251300 2648.198600 2736.680000 3068.365750 3437.434000
max_out_strength 27.0 6045.563033 654.391205 5164.569164 5484.810986 5878.186743 6505.231790 7294.908210
max_total_strength 27.0 8161.270737 874.440626 6936.898164 7421.274986 7994.035743 8708.479297 9908.429210
avg_clus_coef 27.0 0.917879 0.003762 0.910329 0.915375 0.918491 0.920792 0.922678
avg_clus_coef_weight 27.0 0.009799 0.000672 0.008604 0.009299 0.009724 0.010014 0.011400
avg_path_length_for_strong 27.0 1.075397 0.005485 1.066667 1.070238 1.076190 1.078571 1.085714
avg_path_length_weight_for_strong 27.0 1.310632 0.086950 1.145918 1.268590 1.307801 1.351592 1.525382
diameter_for_strong 27.0 2.000000 0.000000 2.000000 2.000000 2.000000 2.000000 2.000000
diameter_weight_for_strong 27.0 12.194128 1.782026 9.102623 10.907103 12.290150 12.891098 16.712108
In [23]:
pd_temportal = pd.DataFrame.from_dict(G_nxs_statistics, orient='index').T
plt.figure(figsize = (24, 6))

plt.subplot(1, 3, 1)
plt.title('avg_total_strength')
plt.xticks(rotation = 80)
plt.plot(pd_temportal.columns.values, pd_temportal.loc['avg_total_strength'])

plt.subplot(1, 3, 2)
plt.title('max_in_strength')
plt.xticks(rotation = 80)
plt.plot(pd_temportal.columns.values, pd_temportal.loc['max_in_strength'])

plt.subplot(1, 3, 3)
plt.title('max_out_strength')
plt.xticks(rotation = 80)
plt.plot(pd_temportal.columns.values, pd_temportal.loc['max_out_strength'])

plt.show()

Inspect with Heterogeneous Statistics¶

In [24]:
G_temp = G_nxs[time_list[0]]
In [25]:
def absolute_filter(G, k):
    G_filtered = nx.subgraph_view(G, filter_edge = lambda s, t: G.edges[s, t]['claims_held'] >= k)

    print(f"Filter loan amount >= {k:.0}:")
    print(f"\t{len(G_filtered.edges)} of {len(G.edges)} edges remain.")
    print(f"\tDensity: {nx.density(G_filtered):.3}")
    print("\tPaths between any node pair:", nx.is_strongly_connected(G_filtered))
    print("\tWeakly connected:", nx.is_weakly_connected(G_filtered))

    return G_filtered

G_1e0 = absolute_filter(G_temp, 1e0)
G_1e1 = absolute_filter(G_temp, 1e1)
G_1e2 = absolute_filter(G_temp, 1e2)
G_1e3 = absolute_filter(G_temp, 1e3)

Filter loan amount >= 1e+00:
	270 of 406 edges remain.
	Density: 0.584
	Paths between any node pair: False
	Weakly connected: True
Filter loan amount >= 1e+01:
	160 of 406 edges remain.
	Density: 0.346
	Paths between any node pair: False
	Weakly connected: True
Filter loan amount >= 1e+02:
	40 of 406 edges remain.
	Density: 0.0866
	Paths between any node pair: False
	Weakly connected: False
Filter loan amount >= 1e+03:
	1 of 406 edges remain.
	Density: 0.00216
	Paths between any node pair: False
	Weakly connected: False
In [26]:
# Identify disconnected countries.
isolates = set(nx.isolates(G_temp))

# Calculate total lending and borrowing.
country_size = sorted(
    list(G_temp.degree(weight = 'claims_held')),
    key = lambda pair: pair[1],
    reverse = True)

plt.figure(figsize = (12, 4))
plt.title('Total Lending and Borrowing')
xticks = np.arange(len(country_size))
plt.bar(xticks, [0 if name in isolates else size for name, size in country_size])
plt.bar(xticks, [size if name in isolates else 0 for name, size in country_size])
plt.xticks(xticks, [name for name, size in country_size], rotation = 45)
plt.ylabel('Node Strength')
plt.show()
In [27]:
def plot_hist(degrees):
    plt.hist([deg for _, deg in degrees])

plt.figure(figsize = (15, 3))

plt.subplot(1, 3, 1)
plt.title('In-strength distribution')
plot_hist(G_temp.in_degree(weight='claims_held'))

plt.subplot(1, 3, 2)
plt.title('Out-strength distribution')
plot_hist(G_temp.out_degree(weight='claims_held'))

plt.subplot(1, 3, 3)
plt.title('Total-strength distribution')
plot_hist(G_temp.degree(weight='claims_held'))

plt.show()
In [28]:
def top_n(deg_dist, n=5):
    return [id for id, _ in sorted(deg_dist, key = lambda p: -p[1])][:n]

pd.DataFrame({
    'In-strength': top_n(G_temp.in_degree(weight='claims_held'),10),
    'Out-strength': top_n(G_temp.out_degree(weight='claims_held'),10),
    'Total-strength': top_n(G_temp.degree(weight='claims_held'),10)
}).T
Out[28]:
0 1 2 3 4 5 6 7 8 9
In-strength Japan United_Kingdom France United_States Germany Switzerland Canada Spain Netherlands Italy
Out-strength United_States United_Kingdom Germany France Japan Italy Netherlands Spain Australia Canada
Total-strength United_States United_Kingdom France Japan Germany Switzerland Canada Spain Netherlands Italy
In [29]:
score_closeness = nx.closeness_centrality(G_temp, distance='claims_held_reciprocal')
In [30]:
score_betweenness = nx.betweenness_centrality(G_temp, weight='claims_held_reciprocal')
In [31]:
pd.DataFrame({
    'Closeness': list(score_closeness.values()),
    'Betweenness': list(score_betweenness.values())
}).describe().T
Out[31]:
count mean std min 25% 50% 75% max
Closeness 22.0 27.279663 16.167909 0.0 10.985898 34.525204 41.838614 45.645066
Betweenness 22.0 0.071320 0.140220 0.0 0.000000 0.000000 0.069643 0.569048
In [32]:
plt.figure(figsize = (10, 3))

plt.suptitle('Centrality Distributions')

plt.subplot(1, 2, 1)
plt.hist(list(score_closeness.values()))
plt.xlabel('Closeness score')
plt.ylabel('Node frequency')

plt.subplot(1, 2, 2)
plt.hist(list(score_betweenness.values()))
plt.xlabel('Betweenness score')
plt.ylabel('Node frequency')

plt.show()

def count_zeros(name, dist):
    n_zero = sum(1 for i in dist if i <= 0)
    print(f"# nodes with zero {name}: {n_zero} ({n_zero/len(dist):.1%})")

count_zeros('closeness', score_closeness.values())
count_zeros('betweenness', score_betweenness.values())

# nodes with zero closeness: 1 (4.5%)
# nodes with zero betweenness: 14 (63.6%)
In [33]:
pd.DataFrame({
    'In-strength': top_n(G_temp.in_degree(weight='claims_held'),10),
    'Out-strength': top_n(G_temp.out_degree(weight='claims_held'),10),
    'Total-strength': top_n(G_temp.degree(weight='claims_held'),10),
    'Closeness': top_n(score_closeness.items(),10),
    'Betweenness': top_n(score_betweenness.items(),10)
}).T
Out[33]:
0 1 2 3 4 5 6 7 8 9
In-strength Japan United_Kingdom France United_States Germany Switzerland Canada Spain Netherlands Italy
Out-strength United_States United_Kingdom Germany France Japan Italy Netherlands Spain Australia Canada
Total-strength United_States United_Kingdom France Japan Germany Switzerland Canada Spain Netherlands Italy
Closeness France Germany United_States Japan United_Kingdom Canada Switzerland Spain Sweden Netherlands
Betweenness United_States United_Kingdom France Germany Spain Sweden Netherlands Italy Australia Austria

Inspect with Community Detection¶

In [34]:
G_temp = G_gts[time_list[0]]
print(G_temp.list_properties())
gt.graph_draw(G_temp,
              vertex_text = G_temp.properties[('v', '_graphml_vertex_id')],
              vertex_size = 10)

_graphml_vertex_id         (vertex)  (type: string)
_graphml_edge_id           (edge)    (type: string)
claims_held                (edge)    (type: long double)
claims_held_reciprocal     (edge)    (type: long double)
None
Out[34]:
<VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc8196c86d0, at 0x7fc80a1c4f10>
In [35]:
state = gt.minimize_nested_blockmodel_dl(G_temp,
              state_args=dict(recs=[G_temp.properties[('e', 'claims_held')]], rec_types=["real-exponential"]))
print(state.entropy())
state.draw(vertex_text = G_temp.properties[('v', '_graphml_vertex_id')],
              vertex_size = 10)

1956.166187611734
Out[35]:
(<VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc8196c86d0, at 0x7fc818df3be0>,
 <GraphView object, directed, with 26 vertices and 25 edges, edges filtered by (<EdgePropertyMap object with value type 'bool', for Graph 0x7fc818dfad00, at 0x7fc80a0cec10>, False), vertices filtered by (<VertexPropertyMap object with value type 'bool', for Graph 0x7fc818dfad00, at 0x7fc80a0ce7f0>, False), at 0x7fc818dfad00>,
 <VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc818dfad00, at 0x7fc80a0cedc0>)
In [36]:
entropys = []
states = []
for i in range(10):
    state = gt.minimize_nested_blockmodel_dl(G_temp,
              state_args=dict(recs=[G_temp.properties[('e', 'claims_held')]], rec_types=["real-exponential"]))
    entropys.append(state.entropy())
    states.append(state)
pd.DataFrame({'entropys': entropys}).describe()
Out[36]:
entropys
count 10.000000
mean 1955.550070
std 9.986092
min 1941.017357
25% 1949.682928
50% 1956.166188
75% 1962.483771
max 1968.344881
In [37]:
index = np.argmin(entropys)
print(index)
print(entropys[index])
states[index].draw(vertex_text = G_temp.properties[('v', '_graphml_vertex_id')],
              vertex_size = 10)

4
1941.017357482232
Out[37]:
(<VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc8196c86d0, at 0x7fc80983b8e0>,
 <GraphView object, directed, with 29 vertices and 28 edges, edges filtered by (<EdgePropertyMap object with value type 'bool', for Graph 0x7fc80a1e0220, at 0x7fc809840c70>, False), vertices filtered by (<VertexPropertyMap object with value type 'bool', for Graph 0x7fc80a1e0220, at 0x7fc809840b50>, False), at 0x7fc80a1e0220>,
 <VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc80a1e0220, at 0x7fc809840760>)
In [38]:
levels = states[index].get_levels()
for s in levels:
    print(s)
    if s.get_N() == 1:
        break

<BlockState object with 22 blocks (4 nonempty), degree-corrected, with 1 edge covariate, for graph <Graph object, directed, with 22 vertices and 406 edges, 1 internal vertex property, 3 internal edge properties, at 0x7fc8196c86d0>, at 0x7fc8098faeb0>
<BlockState object with 4 blocks (2 nonempty), with 1 edge covariate, for graph <Graph object, directed, with 22 vertices and 16 edges, 2 internal vertex properties, 1 internal edge property, at 0x7fc809917340>, at 0x7fc80991ca90>
<BlockState object with 2 blocks (1 nonempty), with 1 edge covariate, for graph <Graph object, directed, with 4 vertices and 4 edges, 2 internal vertex properties, 1 internal edge property, at 0x7fc80991f670>, at 0x7fc80991c940>
<BlockState object with 1 blocks (1 nonempty), with 1 edge covariate, for graph <Graph object, directed, with 2 vertices and 1 edge, 2 internal vertex properties, 1 internal edge property, at 0x7fc8099235e0>, at 0x7fc80991fcd0>

Risk Feature¶

  • Inherent risk & Propagated risk

Feature¶

In [39]:
feature_graphml_dir = 'FNA Feature graphml'
if not os.path.exists(feature_graphml_dir):
    print('*** generate feature graphml')
    os.makedirs(feature_graphml_dir)
    for one_time in time_list:
        G = nx.read_graphml(graphml_dir + "/" + one_time + ".graphml")
        in_strength = G.in_degree(weight = 'claims_held')
        out_strength = G.out_degree(weight = 'claims_held')
        # add norm
        for src, tar, wgt in G.edges.data('claims_held'):
            G.edges[src, tar]['claims_held_norm'] = wgt / out_strength[src]
            G.edges[src, tar]['claims_held_norm_reciprocal'] = 1 / G.edges[src, tar]['claims_held_norm']
        # add inherent risk
        for node in list(G.nodes(data=False)):
            G.nodes[node]['inherent_risk'] = in_strength[node] / out_strength[node]
        # add propagated risk
        propagated_risk = nx.pagerank(G = G.reverse(), # The lender has higher risk, so change the direction
                                      nstart = dict(G.nodes.data('inherent_risk')),
                                      weight = 'claims_held_norm')
        for node in list(G.nodes(data=False)):
            G.nodes[node]['propagated_risk'] = propagated_risk[node]
        nx.write_graphml_lxml(G, feature_graphml_dir + "/" + one_time + ".graphml")

print("*** read graphml for nx")
G_nxs_feature = {}
for one_time in time_list:
    G = nx.read_graphml(feature_graphml_dir + "/" + one_time + ".graphml")
    print("nx time: " + one_time
        + ", nodes: " + str(G.number_of_nodes())
        + ", edges: " + str(G.number_of_edges()))
    print("         " + one_time + ", node attrs: " + str(list(G.nodes.items())[0][1]))
    print("         " + one_time + ", edge attrs: " + str(list(G.edges.items())[0][1]))
    G_nxs_feature[one_time] = G

print("*** read graphml for gt")
G_gts_feature = {}
for one_time in time_list:
    G = gt.load_graph(feature_graphml_dir + "/" + one_time + ".graphml")
    print("gt time: " + one_time
        + ", nodes: " + str(G.num_vertices())
        + ", edges: " + str(G.num_edges()))
    print("         " + one_time
        + ", node attrs: " + str(dict(G.vertex_properties).keys()))
    print("         " + one_time
        + ", edge attrs: " + str(dict(G.edge_properties).keys()))
    G_gts_feature[one_time] = G

*** generate feature graphml
*** read graphml for nx
nx time: 20150331, nodes: 22, edges: 406
         20150331, node attrs: {'inherent_risk': 0.8359096223519187, 'propagated_risk': 0.036327899654037314}
         20150331, edge attrs: {'claims_held': 0.522085, 'claims_held_reciprocal': 1.9153969181263586, 'claims_held_norm': 0.0013394901122495205, 'claims_held_norm_reciprocal': 746.5527299194574}
nx time: 20150630, nodes: 22, edges: 404
         20150630, node attrs: {'inherent_risk': 0.8717347129552802, 'propagated_risk': 0.03620376543272468}
         20150630, edge attrs: {'claims_held': 0.508499, 'claims_held_reciprocal': 1.9665722056483885, 'claims_held_norm': 0.0013148449139959802, 'claims_held_norm_reciprocal': 760.5459696085932}
nx time: 20150930, nodes: 22, edges: 402
         20150930, node attrs: {'inherent_risk': 0.8581957826761578, 'propagated_risk': 0.03510313873428144}
         20150930, edge attrs: {'claims_held': 0.485603, 'claims_held_reciprocal': 2.0592953503170284, 'claims_held_norm': 0.0013257733160539399, 'claims_held_norm_reciprocal': 754.2767589986057}
nx time: 20151231, nodes: 22, edges: 400
         20151231, node attrs: {'inherent_risk': 0.9353228784830633, 'propagated_risk': 0.035493916269102165}
         20151231, edge attrs: {'claims_held': 0.464434, 'claims_held_reciprocal': 2.1531584681569393, 'claims_held_norm': 0.0012678699970503434, 'claims_held_norm_reciprocal': 788.7243978692344}
nx time: 20160331, nodes: 22, edges: 403
         20160331, node attrs: {'inherent_risk': 0.7244609180014627, 'propagated_risk': 0.03607330938040121}
         20160331, edge attrs: {'claims_held': 0.517579, 'claims_held_reciprocal': 1.9320722054024602, 'claims_held_norm': 0.0013396333198742519, 'claims_held_norm_reciprocal': 746.4729229740774}
nx time: 20160630, nodes: 22, edges: 403
         20160630, node attrs: {'inherent_risk': 0.7355449217630071, 'propagated_risk': 0.03669741517811712}
         20160630, edge attrs: {'claims_held': 0.634793, 'claims_held_reciprocal': 1.575316678035202, 'claims_held_norm': 0.0016616117391745262, 'claims_held_norm_reciprocal': 601.8253099829392}
nx time: 20160930, nodes: 22, edges: 400
         20160930, node attrs: {'inherent_risk': 0.6805064251496327, 'propagated_risk': 0.03698837379631897}
         20160930, edge attrs: {'claims_held': 0.655929, 'claims_held_reciprocal': 1.5245552491199506, 'claims_held_norm': 0.0016744784136535128, 'claims_held_norm_reciprocal': 597.2008906451764}
nx time: 20161231, nodes: 22, edges: 402
         20161231, node attrs: {'inherent_risk': 0.7759774696685273, 'propagated_risk': 0.035818653032092224}
         20161231, edge attrs: {'claims_held': 0.594394, 'claims_held_reciprocal': 1.6823857575951306, 'claims_held_norm': 0.0015533879071053572, 'claims_held_norm_reciprocal': 643.7542068055869}
nx time: 20170331, nodes: 22, edges: 399
         20170331, node attrs: {'inherent_risk': 0.7024555590257988, 'propagated_risk': 0.03598888638307345}
         20170331, edge attrs: {'claims_held': 0.556214, 'claims_held_reciprocal': 1.797869165465091, 'claims_held_norm': 0.0013616597055586108, 'claims_held_norm_reciprocal': 734.3978792335324}
nx time: 20170630, nodes: 22, edges: 400
         20170630, node attrs: {'inherent_risk': 0.7002846530256357, 'propagated_risk': 0.0356084115961773}
         20170630, edge attrs: {'claims_held': 0.692545, 'claims_held_reciprocal': 1.4439494906468173, 'claims_held_norm': 0.0016669050847957047, 'claims_held_norm_reciprocal': 599.9141817499222}
nx time: 20170930, nodes: 22, edges: 401
         20170930, node attrs: {'inherent_risk': 0.6635532503651508, 'propagated_risk': 0.03624206599100516}
         20170930, edge attrs: {'claims_held': 0.677814, 'claims_held_reciprocal': 1.4753309905077203, 'claims_held_norm': 0.0015950339847351626, 'claims_held_norm_reciprocal': 626.945889285261}
nx time: 20171231, nodes: 22, edges: 402
         20171231, node attrs: {'inherent_risk': 0.7015242195612428, 'propagated_risk': 0.0353621806241856}
         20171231, edge attrs: {'claims_held': 0.706178, 'claims_held_reciprocal': 1.4160735678539973, 'claims_held_norm': 0.001648147446379585, 'claims_held_norm_reciprocal': 606.7418313796239}
nx time: 20180331, nodes: 22, edges: 401
         20180331, node attrs: {'inherent_risk': 0.6750053496873261, 'propagated_risk': 0.03617604209267839}
         20180331, edge attrs: {'claims_held': 0.765177, 'claims_held_reciprocal': 1.3068871646690896, 'claims_held_norm': 0.0017649920013611048, 'claims_held_norm_reciprocal': 566.5748055678622}
nx time: 20180630, nodes: 22, edges: 403
         20180630, node attrs: {'inherent_risk': 0.7354940253794288, 'propagated_risk': 0.03498572788684408}
         20180630, edge attrs: {'claims_held': 0.721131, 'claims_held_reciprocal': 1.3867105976584007, 'claims_held_norm': 0.0017300779721331088, 'claims_held_norm_reciprocal': 578.0086308867598}
nx time: 20180930, nodes: 22, edges: 405
         20180930, node attrs: {'inherent_risk': 0.663391386304741, 'propagated_risk': 0.03517247461976675}
         20180930, edge attrs: {'claims_held': 0.724015, 'claims_held_reciprocal': 1.381186853863525, 'claims_held_norm': 0.0016866646515013713, 'claims_held_norm_reciprocal': 592.8860838518539}
nx time: 20181231, nodes: 22, edges: 402
         20181231, node attrs: {'inherent_risk': 0.7089821155100179, 'propagated_risk': 0.03622782306546413}
         20181231, edge attrs: {'claims_held': 0.651331, 'claims_held_reciprocal': 1.5353176802578106, 'claims_held_norm': 0.0015306258928652018, 'claims_held_norm_reciprocal': 653.327507826282}
nx time: 20190331, nodes: 22, edges: 407
         20190331, node attrs: {'inherent_risk': 0.6119777507755584, 'propagated_risk': 0.03594987272278945}
         20190331, edge attrs: {'claims_held': 0.669325, 'claims_held_reciprocal': 1.4940425055092819, 'claims_held_norm': 0.0015312227675064877, 'claims_held_norm_reciprocal': 653.0728390542711}
nx time: 20190630, nodes: 22, edges: 404
         20190630, node attrs: {'inherent_risk': 0.6008645652869773, 'propagated_risk': 0.03642819572685735}
         20190630, edge attrs: {'claims_held': 0.727638, 'claims_held_reciprocal': 1.3743097529265926, 'claims_held_norm': 0.0016416134144234473, 'claims_held_norm_reciprocal': 609.1568156143577}
nx time: 20190930, nodes: 22, edges: 408
         20190930, node attrs: {'inherent_risk': 0.6267124978706184, 'propagated_risk': 0.035810238460497155}
         20190930, edge attrs: {'claims_held': 0.705982, 'claims_held_reciprocal': 1.4164667087829435, 'claims_held_norm': 0.0016122530261698952, 'claims_held_norm_reciprocal': 620.2500375363678}
nx time: 20191231, nodes: 22, edges: 406
         20191231, node attrs: {'inherent_risk': 0.6838906957539285, 'propagated_risk': 0.03598218968189507}
         20191231, edge attrs: {'claims_held': 0.680489, 'claims_held_reciprocal': 1.469531469281649, 'claims_held_norm': 0.0015027868124710415, 'claims_held_norm_reciprocal': 665.4303802118772}
nx time: 20200331, nodes: 22, edges: 409
         20200331, node attrs: {'inherent_risk': 0.6954238388004949, 'propagated_risk': 0.03487145069027153}
         20200331, edge attrs: {'claims_held': 0.690694, 'claims_held_reciprocal': 1.4478191500143334, 'claims_held_norm': 0.0015241460987777985, 'claims_held_norm_reciprocal': 656.105081266089}
nx time: 20200630, nodes: 22, edges: 408
         20200630, node attrs: {'inherent_risk': 0.6204131147998669, 'propagated_risk': 0.033923847675701294}
         20200630, edge attrs: {'claims_held': 0.867392, 'claims_held_reciprocal': 1.1528812808972182, 'claims_held_norm': 0.001768669482294555, 'claims_held_norm_reciprocal': 565.3967629399394}
nx time: 20200930, nodes: 22, edges: 406
         20200930, node attrs: {'inherent_risk': 0.6001195333484551, 'propagated_risk': 0.03399973359936588}
         20200930, edge attrs: {'claims_held': 0.746455, 'claims_held_reciprocal': 1.3396654855282637, 'claims_held_norm': 0.001521718449345018, 'claims_held_norm_reciprocal': 657.1517881185068}
nx time: 20201231, nodes: 22, edges: 408
         20201231, node attrs: {'inherent_risk': 0.6431382953593519, 'propagated_risk': 0.034350483406970306}
         20201231, edge attrs: {'claims_held': 0.706643, 'claims_held_reciprocal': 1.4151417335203207, 'claims_held_norm': 0.0013248451933569362, 'claims_held_norm_reciprocal': 754.8051689466957}
nx time: 20210331, nodes: 22, edges: 405
         20210331, node attrs: {'inherent_risk': 0.5439169653898268, 'propagated_risk': 0.03239908325466501}
         20210331, edge attrs: {'claims_held': 0.556745, 'claims_held_reciprocal': 1.79615443335818, 'claims_held_norm': 0.0010313662800666675, 'claims_held_norm_reciprocal': 969.5876424574983}
nx time: 20210630, nodes: 22, edges: 407
         20210630, node attrs: {'inherent_risk': 0.5668552464780188, 'propagated_risk': 0.03427402842815736}
         20210630, edge attrs: {'claims_held': 0.536295, 'claims_held_reciprocal': 1.8646453910627547, 'claims_held_norm': 0.0009826939837594112, 'claims_held_norm_reciprocal': 1017.6107888382329}
nx time: 20210930, nodes: 22, edges: 407
         20210930, node attrs: {'inherent_risk': 0.5392443909252684, 'propagated_risk': 0.03337062656640623}
         20210930, edge attrs: {'claims_held': 0.468677, 'claims_held_reciprocal': 2.1336656161919616, 'claims_held_norm': 0.0008847816844231451, 'claims_held_norm_reciprocal': 1130.2223108878823}
*** read graphml for gt
gt time: 20150331, nodes: 22, edges: 406
         20150331, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20150331, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20150630, nodes: 22, edges: 404
         20150630, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20150630, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20150930, nodes: 22, edges: 402
         20150930, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20150930, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20151231, nodes: 22, edges: 400
         20151231, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20151231, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20160331, nodes: 22, edges: 403
         20160331, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20160331, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20160630, nodes: 22, edges: 403
         20160630, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20160630, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20160930, nodes: 22, edges: 400
         20160930, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20160930, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20161231, nodes: 22, edges: 402
         20161231, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20161231, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20170331, nodes: 22, edges: 399
         20170331, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20170331, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20170630, nodes: 22, edges: 400
         20170630, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20170630, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20170930, nodes: 22, edges: 401
         20170930, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20170930, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20171231, nodes: 22, edges: 402
         20171231, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20171231, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20180331, nodes: 22, edges: 401
         20180331, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20180331, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20180630, nodes: 22, edges: 403
         20180630, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20180630, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20180930, nodes: 22, edges: 405
         20180930, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20180930, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20181231, nodes: 22, edges: 402
         20181231, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20181231, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20190331, nodes: 22, edges: 407
         20190331, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20190331, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20190630, nodes: 22, edges: 404
         20190630, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20190630, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20190930, nodes: 22, edges: 408
         20190930, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20190930, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20191231, nodes: 22, edges: 406
         20191231, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20191231, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20200331, nodes: 22, edges: 409
         20200331, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20200331, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20200630, nodes: 22, edges: 408
         20200630, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20200630, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20200930, nodes: 22, edges: 406
         20200930, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20200930, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20201231, nodes: 22, edges: 408
         20201231, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20201231, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20210331, nodes: 22, edges: 405
         20210331, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20210331, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20210630, nodes: 22, edges: 407
         20210630, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20210630, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])
gt time: 20210930, nodes: 22, edges: 407
         20210930, node attrs: dict_keys(['_graphml_vertex_id', 'inherent_risk', 'propagated_risk'])
         20210930, edge attrs: dict_keys(['_graphml_edge_id', 'claims_held', 'claims_held_norm', 'claims_held_norm_reciprocal', 'claims_held_reciprocal'])

Visualization¶

In [40]:
G_temp = G_nxs_feature[time_list[0]]
In [41]:
def disparity_filter(G, alpha):
    s = G.out_degree(weight = 'claims_held')
    k = G.out_degree(weight = None)

    def pij(i, j):
        w = G.edges[i, j]['claims_held']
        return ((1 - (w / s[i])) ** (k[i] - 1)) < alpha

    return nx.subgraph_view(G, filter_edge = pij)


G_filt = disparity_filter(G_temp, .1)
print('Filtered network:', len(G_filt.edges), 'edges remain out of', len(G_temp.edges))

plt.figure(3, figsize = (10, 20))
plt.subplot(2, 1, 1)
plt.title('Inherent Risk')
nx.draw(
  G_filt,
  pos = nx.circular_layout(G_filt),
  node_size=1500,
  node_color = [wgt for _, wgt in G_filt.nodes.data('inherent_risk')],
  cmap = mpl.cm.coolwarm,
  with_labels = True,
  font_color = 'black',
  font_size = 10,
  edge_color = [np.log(wgt) for _, _, wgt in G_filt.edges.data('claims_held')],
  edge_cmap = mpl.cm.coolwarm,
  arrowsize = 15,
  connectionstyle="arc3,rad=0.1")

plt.subplot(2, 1, 2)
plt.title('Propagated Risk')
nx.draw(
  G_filt,
  pos = nx.circular_layout(G_filt),
  node_size=1500,
  node_color = [wgt for _, wgt in G_filt.nodes.data('propagated_risk')],
  cmap = mpl.cm.coolwarm,
  with_labels = True,
  font_color = 'black',
  font_size = 10,
  edge_color = [np.log(wgt) for _, _, wgt in G_filt.edges.data('claims_held')],
  edge_cmap = mpl.cm.coolwarm,
  arrowsize = 15,
  connectionstyle="arc3,rad=0.1")
plt.show()

Filtered network: 60 edges remain out of 406
In [42]:
# Japan in
G_filt.in_edges('Japan',data='claims_held_norm')
Out[42]:
InEdgeDataView([('Australia', 'Japan', 0.2630001866103677), ('Canada', 'Japan', 0.1632493233762417), ('France', 'Japan', 0.1583340820653159), ('South_Korea', 'Japan', 0.21206383293224682), ('Netherlands', 'Japan', 0.12801184163062135), ('Sweden', 'Japan', 0.1590112077574935), ('United_States', 'Japan', 0.25687145260347677)])
In [43]:
# Switzerland in
G_filt.in_edges('Switzerland',data='claims_held_norm')
Out[43]:
InEdgeDataView([])
In [44]:
# Sweden in
G_filt.in_edges('Sweden',data='claims_held_norm')
Out[44]:
InEdgeDataView([('Finland', 'Sweden', 0.6107958070101474)])
In [45]:
# Greece in
G_filt.in_edges('Greece',data='claims_held_norm')
Out[45]:
InEdgeDataView([('Turkey', 'Greece', 0.15875132337244569)])
In [46]:
G_filt.out_edges('United_States',data='claims_held_norm')
Out[46]:
OutEdgeDataView([('United_States', 'Canada', 0.1410859036275138), ('United_States', 'United_Kingdom', 0.17598350025983786), ('United_States', 'Japan', 0.25687145260347677)])

Static Analysis¶

Different insights from previous networks¶

Distribution for total normalized lending and borrowing¶

In [47]:
G_temp = G_nxs_feature[time_list[0]]
In [48]:
# Identify disconnected countries.
isolates = set(nx.isolates(G_temp))

# Calculate total strength.
country_size = sorted(
    list(G_temp.degree(weight = 'claims_held_norm')),
    key = lambda pair: pair[1],
    reverse = True)

plt.figure(figsize = (12, 4))
plt.title('Total Normalized Lending and Borrowing')
xticks = np.arange(len(country_size))
plt.bar(xticks, [0 if name in isolates else size for name, size in country_size])
plt.bar(xticks, [size if name in isolates else 0 for name, size in country_size])
plt.xticks(xticks, [name for name, size in country_size], rotation = 45)
plt.ylabel('Node Strength')
plt.show()

Central Nodes¶

In [49]:
score_closeness = nx.closeness_centrality(G_temp, distance='claims_held_norm_reciprocal')
score_betweenness = nx.betweenness_centrality(G_temp, weight='claims_held_norm_reciprocal')

pd.DataFrame({
    'In-strength': top_n(G_temp.in_degree(weight='claims_held_norm'),10),
    'Out-strength': top_n(G_temp.out_degree(weight='claims_held_norm'),10),
    'Total-strength': top_n(G_temp.degree(weight='claims_held_norm'),10),
    'Closeness': top_n(score_closeness.items(),10),
    'Betweenness': top_n(score_betweenness.items(),10)
}).T
Out[49]:
0 1 2 3 4 5 6 7 8 9
In-strength United_States France United_Kingdom Germany Japan Spain Netherlands Italy Sweden Switzerland
Out-strength Spain Australia Belgium Switzerland Germany France Finland United_Kingdom India South_Korea
Total-strength United_States France United_Kingdom Germany Japan Spain Netherlands Italy Sweden Switzerland
Closeness United_States France United_Kingdom Germany Japan Spain Canada Netherlands Italy Switzerland
Betweenness United_Kingdom Germany France United_States Spain Netherlands Sweden Japan Italy Greece

Communities¶

In [50]:
G_temp = G_gts_feature[time_list[0]]
In [51]:
entropys = []
states = []
for i in range(10):
  state = gt.minimize_nested_blockmodel_dl(G_temp,
              state_args=dict(recs=[G_temp.properties[('e', 'claims_held_norm_reciprocal')]], rec_types=["real-exponential"]))
  entropys.append(state.entropy())
  states.append(state)
pd.DataFrame({'entropys': entropys}).describe()
Out[51]:
entropys
count 10.000000
mean 3677.656510
std 93.886704
min 3616.473103
25% 3616.769599
50% 3616.769599
75% 3712.106115
max 3880.131417
In [52]:
index = np.argmin(entropys)
print(index)
print(entropys[index])
states[index].draw(vertex_text = G_temp.properties[('v', '_graphml_vertex_id')],
              vertex_size = 10)

8
3616.473102697209
Out[52]:
(<VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc80a1a5820, at 0x7fc80976e250>,
 <GraphView object, directed, with 28 vertices and 27 edges, edges filtered by (<EdgePropertyMap object with value type 'bool', for Graph 0x7fc80976e340, at 0x7fc8097382e0>, False), vertices filtered by (<VertexPropertyMap object with value type 'bool', for Graph 0x7fc80976e340, at 0x7fc80976cf70>, False), at 0x7fc80976e340>,
 <VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc80976e340, at 0x7fc80976cdc0>)

Cross-sectional Analysis¶

Inherent and Propagated Risks¶

In [53]:
# 2021.03.31 within COVID-19
G_temp = G_nxs_feature['20210331']
In [54]:
def disparity_filter(G, alpha):
    s = G.out_degree(weight = 'claims_held')
    k = G.out_degree(weight = None)

    def pij(i, j):
        w = G.edges[i, j]['claims_held']
        return ((1 - (w / s[i])) ** (k[i] - 1)) < alpha

    return nx.subgraph_view(G, filter_edge = pij)


G_filt = disparity_filter(G_temp, .1)
print('Filtered network:', len(G_filt.edges), 'edges remain out of', len(G_temp.edges))

plt.figure(3, figsize = (10, 20))
plt.subplot(2, 1, 1)
plt.title('Inherent Risk')
nx.draw(
  G_filt,
  pos = nx.circular_layout(G_filt),
  node_size=1500,
  node_color = [wgt for _, wgt in G_filt.nodes.data('inherent_risk')],
  cmap = mpl.cm.coolwarm,
  with_labels = True,
  font_color = 'black',
  font_size = 10,
  edge_color = [np.log(wgt) for _, _, wgt in G_filt.edges.data('claims_held')],
  edge_cmap = mpl.cm.coolwarm,
  arrowsize = 15,
  connectionstyle="arc3,rad=0.1")

plt.subplot(2, 1, 2)
plt.title('Propagated Risk')
nx.draw(
  G_filt,
  pos = nx.circular_layout(G_filt),
  node_size=1500,
  node_color = [wgt for _, wgt in G_filt.nodes.data('propagated_risk')],
  cmap = mpl.cm.coolwarm,
  with_labels = True,
  font_color = 'black',
  font_size = 10,
  edge_color = [np.log(wgt) for _, _, wgt in G_filt.edges.data('claims_held')],
  edge_cmap = mpl.cm.coolwarm,
  arrowsize = 15,
  connectionstyle="arc3,rad=0.1")
plt.show()

Filtered network: 64 edges remain out of 405
In [55]:
pd.DataFrame({
    'inherent_risk': [id for id,  wgt in sorted(G_filt.nodes.data('inherent_risk'), key = lambda p: -p[1])][:15],
    'propagated': [id for id,  wgt in sorted(G_filt.nodes.data('propagated_risk'), key = lambda p: -p[1])][:15]
}).T
Out[55]:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
inherent_risk Canada Spain Japan Switzerland Netherlands France Greece Sweden United_Kingdom Italy Germany Austria Australia United_States Belgium
propagated United_Kingdom Spain Greece Germany France Finland Netherlands United_States Ireland Austria Italy Switzerland Canada Sweden Portugal
In [56]:
G_filt.in_edges(['Spain'], data='claims_held')
Out[56]:
InEdgeDataView([('Chile', 'Spain', 66.549508), ('United_Kingdom', 'Spain', 498.325), ('Italy', 'Spain', 109.265), ('Portugal', 'Spain', 124.96), ('Turkey', 'Spain', 59.869408)])
In [57]:
G_filt.out_edges(['Portugal'], data='claims_held_norm')
Out[57]:
OutEdgeDataView([('Portugal', 'Spain', 0.7036374304976443), ('Portugal', 'France', 0.14089078223816867)])
In [58]:
G_filt.out_edges(['Greece'], data='claims_held_norm')
Out[58]:
OutEdgeDataView([('Greece', 'Germany', 0.22919726293271056), ('Greece', 'United_States', 0.16489579329754392)])

Time series Analysis¶

Communities¶

In [59]:
G_20190331 = G_gts_feature['20190331']
G_20210331 = G_gts_feature['20210331']
In [60]:
entropys_20190331 = []
states_20190331 = []
entropys_20210331 = []
states_20210331 = []
for i in range(10):
    state = gt.minimize_nested_blockmodel_dl(G_20190331,
              state_args=dict(recs=[G_20190331.properties[('e', 'claims_held_norm_reciprocal')]], rec_types=["real-exponential"]))
    entropys_20190331.append(state.entropy())
    states_20190331.append(state)
for i in range(10):
    state = gt.minimize_nested_blockmodel_dl(G_20210331,
              state_args=dict(recs=[G_20210331.properties[('e', 'claims_held_norm_reciprocal')]], rec_types=["real-exponential"]))
    entropys_20210331.append(state.entropy())
    states_20210331.append(state)
pd.DataFrame({'entropys_20190331': entropys_20190331, 'entropys_20210331':entropys_20210331}).describe().T
Out[60]:
count mean std min 25% 50% 75% max
entropys_20190331 10.0 3648.298268 40.483176 3606.227104 3616.253145 3636.570287 3678.204710 3719.649394
entropys_20210331 10.0 3632.736994 117.436178 3591.627352 3591.627352 3591.627352 3603.667324 3966.256348
In [61]:
index_20190331 = np.argmin(entropys_20190331)
states_20190331[index_20190331].draw(vertex_text = G_20190331.properties[('v', '_graphml_vertex_id')],
              vertex_size = 10)
Out[61]:
(<VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc80a221940, at 0x7fc80a391910>,
 <GraphView object, directed, with 28 vertices and 27 edges, edges filtered by (<EdgePropertyMap object with value type 'bool', for Graph 0x7fc8180cef10, at 0x7fc809259ac0>, False), vertices filtered by (<VertexPropertyMap object with value type 'bool', for Graph 0x7fc8180cef10, at 0x7fc8092599a0>, False), at 0x7fc8180cef10>,
 <VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc8180cef10, at 0x7fc809259160>)
In [62]:
index_20210331 = np.argmin(entropys_20210331)
states_20210331[index_20210331].draw(vertex_text = G_20210331.properties[('v', '_graphml_vertex_id')],
              vertex_size = 10)
Out[62]:
(<VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc80a2144f0, at 0x7fc809256d00>,
 <GraphView object, directed, with 28 vertices and 27 edges, edges filtered by (<EdgePropertyMap object with value type 'bool', for Graph 0x7fc80a412b50, at 0x7fc80925e850>, False), vertices filtered by (<VertexPropertyMap object with value type 'bool', for Graph 0x7fc80a412b50, at 0x7fc80925eaf0>, False), at 0x7fc80a412b50>,
 <VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc80a412b50, at 0x7fc80925ea60>)
Analyze Canada and Portugal¶
In [63]:
# Canada and Portugal
# Canada out
data_to_add = []
df_2019 = pd.DataFrame(columns=['out country', '20190331 claims_held', '20190331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20190331'].edges('Canada', data=True):
    data_to_add.append({'out country':des,
             '20190331 claims_held':attr_dict['claims_held'],
             '20190331 claims_held_norm':attr_dict['claims_held_norm']})
df_2019 = pd.concat([df_2019, pd.DataFrame(data_to_add)], ignore_index=True)

data_to_add = []
df_2021 = pd.DataFrame(columns=['out country', '20210331 claims_held', '20210331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20210331'].edges('Canada', data=True):
    data_to_add.append({'out country':des,
             '20210331 claims_held':attr_dict['claims_held'],
             '20210331 claims_held_norm':attr_dict['claims_held_norm']})
df_2021 = pd.concat([df_2021, pd.DataFrame(data_to_add)], ignore_index=True)

df_Canada_out = df_2019.merge(df_2021, how='outer', on=['out country'])
df_Canada_out['claims_diff'] = df_Canada_out['20210331 claims_held'] - df_Canada_out['20190331 claims_held']
df_Canada_out[['out country',
           '20190331 claims_held','20210331 claims_held',
           '20190331 claims_held_norm','20210331 claims_held_norm',
           'claims_diff']]
Out[63]:
out country 20190331 claims_held 20210331 claims_held 20190331 claims_held_norm 20210331 claims_held_norm claims_diff
0 Austria 1.326616 1.791729 0.002989 0.003174 0.465113
1 Australia 11.312021 13.157539 0.025485 0.023306 1.845518
2 Belgium 3.325 4.83 0.007491 0.008555 1.505
3 Switzerland 23.986149 29.811022 0.054038 0.052805 5.824873
4 Chile 0.059385 0.029754 0.000134 0.000053 -0.029631
5 Germany 34.167 38.868 0.076975 0.068847 4.701
6 Spain 4.715695 5.201965 0.010624 0.009214 0.48627
7 Finland 3.066 3.532 0.006907 0.006256 0.466
8 France 30.368 36.636 0.068416 0.064894 6.268
9 United_Kingdom 99.638 127.598 0.224474 0.226015 27.96
10 Greece 0.048 0.02 0.000108 0.000035 -0.028
11 Ireland 1.625071 2.011818 0.003661 0.003564 0.386747
12 Italy 2.479197 2.956778 0.005585 0.005237 0.477581
13 Japan 76.2832 101.892 0.171858 0.180482 25.6088
14 South_Korea 3.016028 4.496539 0.006795 0.007965 1.480511
15 Netherlands 14.591781 18.667296 0.032874 0.033066 4.075515
16 Portugal 0.124766 0.132552 0.000281 0.000235 0.007786
17 Sweden 2.43288 0.792652 0.005481 0.001404 -1.640228
18 Turkey 0.014394 0.031848 0.000032 0.000056 0.017454
19 United_States 131.295 172.097 0.295793 0.304837 40.802
In [64]:
# Canada in
data_to_add = []
df_2019 = pd.DataFrame(columns=['in country', '20190331 claims_held', '20190331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20190331'].in_edges('Canada', data=True):
    data_to_add.append({'in country':src,
             '20190331 claims_held':attr_dict['claims_held'],
             '20190331 claims_held_norm':attr_dict['claims_held_norm']})
df_2019 = pd.concat([df_2019, pd.DataFrame(data_to_add)], ignore_index=True)

data_to_add = []
df_2021 = pd.DataFrame(columns=['in country', '20210331 claims_held', '20210331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20210331'].in_edges('Canada', data=True):
    data_to_add.append({'in country':src,
             '20210331 claims_held':attr_dict['claims_held'],
             '20210331 claims_held_norm':attr_dict['claims_held_norm']})
df_2021 = pd.concat([df_2021, pd.DataFrame(data_to_add)], ignore_index=True)

df_Canada_in = df_2019.merge(df_2021, how='outer', on=['in country'])
df_Canada_in['claims_diff'] = df_Canada_in['20210331 claims_held'] - df_Canada_in['20190331 claims_held']
df_Canada_in[['in country',
           '20190331 claims_held','20210331 claims_held',
           '20190331 claims_held_norm','20210331 claims_held_norm',
           'claims_diff']]
Out[64]:
in country 20190331 claims_held 20210331 claims_held 20190331 claims_held_norm 20210331 claims_held_norm claims_diff
0 Australia 21.147346 22.575065 0.048379 0.04182 1.427719
1 Austria 1.919362 2.327722 0.010432 0.010121 0.40836
2 Belgium 2.263015 1.546472 0.005943 0.00343 -0.716543
3 Switzerland 8.984105 15.117394 0.024047 0.036245 6.133289
4 Germany 32.363637 25.810481 0.023281 0.014946 -6.553156
5 Spain 1.732413 2.006919 0.004242 0.004009 0.274506
6 Finland 2.367553 2.398883 0.017422 0.015812 0.03133
7 France 25.279107 32.708234 0.020607 0.021706 7.429127
8 United_Kingdom 126.916 182.298 0.05601 0.072208 55.382
9 Ireland 30.934869 39.82974 0.07116 0.07394 8.894871
10 Italy 1.574582 0.495262 0.002303 0.000637 -1.07932
11 Japan 40.974525 48.412514 0.039447 0.040436 7.437989
12 South_Korea 1.209863 1.195375 0.004339 0.003598 -0.014488
13 Netherlands 8.688485 8.95013 0.017713 0.017262 0.261645
14 Sweden 7.335088 6.347792 0.054644 0.043315 -0.987296
15 United_States 1168.04 1459.4 0.189107 0.202203 291.36
16 Greece NaN 0.000472 NaN 0.000027 NaN
In [65]:
# Portugal out
data_to_add = []
df_2019 = pd.DataFrame(columns=['out country', '20190331 claims_held', '20190331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20190331'].edges('Portugal', data=True):
    data_to_add.append({'out country':des,
             '20190331 claims_held':attr_dict['claims_held'],
             '20190331 claims_held_norm':attr_dict['claims_held_norm']})
df_2019 = pd.concat([df_2019, pd.DataFrame(data_to_add)], ignore_index=True)

data_to_add = []
df_2021 = pd.DataFrame(columns=['out country', '20210331 claims_held', '20210331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20210331'].edges('Portugal', data=True):
    data_to_add.append({'out country':des,
             '20210331 claims_held':attr_dict['claims_held'],
             '20210331 claims_held_norm':attr_dict['claims_held_norm']})
df_2021 = pd.concat([df_2021, pd.DataFrame(data_to_add)], ignore_index=True)

df_Portugal_out = df_2019.merge(df_2021, how='outer', on=['out country'])
df_Portugal_out['claims_diff'] = df_Portugal_out['20210331 claims_held'] - df_Portugal_out['20190331 claims_held']
df_Portugal_out[['out country',
           '20190331 claims_held','20210331 claims_held',
           '20190331 claims_held_norm','20210331 claims_held_norm',
           'claims_diff']]
Out[65]:
out country 20190331 claims_held 20210331 claims_held 20190331 claims_held_norm 20210331 claims_held_norm claims_diff
0 Austria 0.362732 0.362664 0.002408 0.002042 -0.000068
1 Australia 0.011246 0.10485 0.000075 0.00059 0.093604
2 Belgium 0.46 0.559 0.003053 0.003148 0.099
3 Germany 9.92 8.905 0.065847 0.050143 -1.015
4 Spain 105.147 124.96 0.697946 0.703637 19.813
5 Finland 0.048 0.137 0.000319 0.000771 0.089
6 France 18.722 25.021 0.124273 0.140891 6.299
7 United_Kingdom 1.667 1.082 0.011065 0.006093 -0.585
8 Greece 0.367 0.469 0.002436 0.002641 0.102
9 Ireland 0.572673 1.257716 0.003801 0.007082 0.685043
10 Italy 5.704083 7.472428 0.037863 0.042077 1.768345
11 Japan 1.1256 1.4374 0.007472 0.008094 0.3118
12 South_Korea 0.082988 0.030305 0.000551 0.000171 -0.052683
13 Netherlands 2.255572 1.99799 0.014972 0.01125 -0.257582
14 Sweden 0.128055 0.183319 0.00085 0.001032 0.055264
15 Turkey 0.002215 0.00079 0.000015 0.000004 -0.001425
16 United_States 4.076 3.611 0.027056 0.020333 -0.465
In [66]:
# Portugal in
data_to_add = []
df_2019 = pd.DataFrame(columns=['in country', '20190331 claims_held', '20190331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20190331'].in_edges('Portugal', data=True):
    data_to_add.append({'in country':src,
             '20190331 claims_held':attr_dict['claims_held'],
             '20190331 claims_held_norm':attr_dict['claims_held_norm']})
df_2019 = pd.concat([df_2019, pd.DataFrame(data_to_add)], ignore_index=True)

data_to_add = []
df_2021 = pd.DataFrame(columns=['in country', '20210331 claims_held', '20210331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20210331'].in_edges('Portugal', data=True):
    data_to_add.append({'in country':src,
             '20210331 claims_held':attr_dict['claims_held'],
             '20210331 claims_held_norm':attr_dict['claims_held_norm']})
df_2021 = pd.concat([df_2021, pd.DataFrame(data_to_add)], ignore_index=True)

df_Portugal_in = df_2019.merge(df_2021, how='outer', on=['in country'])
df_Portugal_in['claims_diff'] = df_Portugal_in['20210331 claims_held'] - df_Portugal_in['20190331 claims_held']
df_Portugal_in[['in country',
           '20190331 claims_held','20210331 claims_held',
           '20190331 claims_held_norm','20210331 claims_held_norm',
           'claims_diff']]
Out[66]:
in country 20190331 claims_held 20210331 claims_held 20190331 claims_held_norm 20210331 claims_held_norm claims_diff
0 Australia 0.136822 0.078891 0.000313 0.000146 -0.057931
1 Austria 0.1844 0.303853 0.001002 0.001321 0.119453
2 Belgium 0.553313 0.351384 0.001453 0.000779 -0.201929
3 Canada 0.124766 0.132552 0.000281 0.000235 0.007786
4 Switzerland 1.819297 2.225883 0.00487 0.005337 0.406586
5 Chile 0.045116 0.059417 0.000529 0.000644 0.014301
6 Germany 2.474712 2.717083 0.00178 0.001573 0.242371
7 Spain 18.480084 16.967643 0.045247 0.033891 -1.512441
8 Finland 0.201811 0.315824 0.001485 0.002082 0.114013
9 France 5.711607 7.065255 0.004656 0.004689 1.353648
10 United_Kingdom 2.220809 2.492629 0.00098 0.000987 0.27182
11 Greece 0.2093 0.515956 0.00728 0.029077 0.306656
12 Ireland 1.542329 1.845977 0.003548 0.003427 0.303648
13 India 0.07329 0.089081 0.000285 0.000371 0.015791
14 Italy 8.611367 12.246638 0.012593 0.015748 3.635271
15 Japan 0.141101 0.213069 0.000136 0.000178 0.071968
16 South_Korea 0.000943 0.031935 0.000003 0.000096 0.030992
17 Netherlands 1.590697 2.689452 0.003243 0.005187 1.098755
18 Sweden 0.154093 0.205281 0.001148 0.001401 0.051188
19 Turkey 0.233778 0.223205 0.001549 0.001719 -0.010573
20 United_States 1.863351 2.762204 0.000302 0.000383 0.898853
In [67]:
# Italy out
data_to_add = []
df_2019 = pd.DataFrame(columns=['out country', '20190331 claims_held', '20190331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20190331'].edges('Italy', data=True):
    data_to_add.append({'out country':des,
             '20190331 claims_held':attr_dict['claims_held'],
             '20190331 claims_held_norm':attr_dict['claims_held_norm']})
df_2019 = pd.concat([df_2019, pd.DataFrame(data_to_add)], ignore_index=True)

data_to_add = []
df_2021 = pd.DataFrame(columns=['out country', '20210331 claims_held', '20210331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20210331'].edges('Italy', data=True):
    data_to_add.append({'out country':des,
             '20210331 claims_held':attr_dict['claims_held'],
             '20210331 claims_held_norm':attr_dict['claims_held_norm']})
df_2021 = pd.concat([df_2021, pd.DataFrame(data_to_add)], ignore_index=True)

df_Italy_out = df_2019.merge(df_2021, how='outer', on=['out country'])
df_Italy_out['claims_diff'] = df_Italy_out['20210331 claims_held'] - df_Italy_out['20190331 claims_held']
df_Italy_out[['out country',
           '20190331 claims_held','20210331 claims_held',
           '20190331 claims_held_norm','20210331 claims_held_norm',
           'claims_diff']]
Out[67]:
out country 20190331 claims_held 20210331 claims_held 20190331 claims_held_norm 20210331 claims_held_norm claims_diff
0 Austria 4.919401 5.453861 0.007194 0.007013 0.53446
1 Australia 0.227788 0.390702 0.000333 0.000502 0.162914
2 Belgium 4.75 4.02 0.006946 0.005169 -0.73
3 Canada 1.574582 0.495262 0.002303 0.000637 -1.07932
4 Switzerland 15.549292 17.14311 0.022739 0.022044 1.593818
5 Chile 0.006028 0.005978 0.000009 0.000008 -0.00005
6 Germany 89.776 89.87 0.131288 0.115561 0.094
7 Spain 74.76027 109.265 0.109329 0.140501 34.50473
8 Finland 0.184 NaN 0.000269 NaN NaN
9 France 327.308 372.293 0.478652 0.47872 44.985
10 United_Kingdom 31.182 19.494 0.0456 0.025067 -11.688
11 Greece 3.513 6.933 0.005137 0.008915 3.42
12 Ireland 1.572325 0.604465 0.002299 0.000777 -0.96786
13 Japan 33.8155 52.7713 0.049451 0.067857 18.9558
14 South_Korea 0.237425 0.226043 0.000347 0.000291 -0.011382
15 Netherlands 27.997413 25.653616 0.040943 0.032987 -2.343797
16 Portugal 8.611367 12.246638 0.012593 0.015748 3.635271
17 Sweden 0.130025 0.070025 0.00019 0.00009 -0.06
18 Turkey 0.23257 0.129022 0.00034 0.000166 -0.103548
19 United_States 57.465 60.619 0.084036 0.077948 3.154
In [68]:
# Italy in
data_to_add = []
df_2019 = pd.DataFrame(columns=['in country', '20190331 claims_held', '20190331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20190331'].in_edges('Italy', data=True):
    data_to_add.append({'in country':src,
             '20190331 claims_held':attr_dict['claims_held'],
             '20190331 claims_held_norm':attr_dict['claims_held_norm']})
df_2019 = pd.concat([df_2019, pd.DataFrame(data_to_add)], ignore_index=True)

data_to_add = []
df_2021 = pd.DataFrame(columns=['in country', '20210331 claims_held', '20210331 claims_held_norm'])
for src, des, attr_dict in G_nxs_feature['20210331'].in_edges('Italy', data=True):
    data_to_add.append({'in country':src,
             '20210331 claims_held':attr_dict['claims_held'],
             '20210331 claims_held_norm':attr_dict['claims_held_norm']})
df_2021 = pd.concat([df_2021, pd.DataFrame(data_to_add)], ignore_index=True)

df_Italy_in = df_2019.merge(df_2021, how='outer', on=['in country'])
df_Italy_in['claims_diff'] = df_Italy_in['20210331 claims_held'] - df_Italy_in['20190331 claims_held']
df_Italy_in[['in country',
           '20190331 claims_held','20210331 claims_held',
           '20190331 claims_held_norm','20210331 claims_held_norm',
           'claims_diff']]
Out[68]:
in country 20190331 claims_held 20210331 claims_held 20190331 claims_held_norm 20210331 claims_held_norm claims_diff
0 Australia 1.147752 2.397472 0.002626 0.004441 1.24972
1 Austria 80.254893 106.797 0.436211 0.464374 26.542107
2 Belgium 8.917215 12.505413 0.023419 0.027738 3.588198
3 Canada 2.479197 2.956778 0.005585 0.005237 0.477581
4 Switzerland 15.239844 18.580399 0.040792 0.044548 3.340555
5 Chile 0.349842 NaN 0.004099 NaN NaN
6 Germany 167.188 230.738 0.120266 0.133614 63.55
7 Spain 62.303733 86.446939 0.152547 0.172667 24.143206
8 Finland 1.936336 2.85662 0.014249 0.018829 0.920284
9 France 63.310806 68.394058 0.051609 0.045388 5.083252
10 United_Kingdom 46.445994 40.219739 0.020497 0.015931 -6.226255
11 Greece 2.53233 1.371391 0.088077 0.077285 -1.160939
12 Ireland 11.116013 18.954244 0.02557 0.035187 7.838231
13 India 1.462469 1.51807 0.005688 0.006317 0.055601
14 Japan 14.821657 19.659433 0.014269 0.01642 4.837776
15 South_Korea 0.326356 2.085503 0.00117 0.006277 1.759147
16 Netherlands 18.615587 26.788284 0.037951 0.051666 8.172697
17 Portugal 5.704083 7.472428 0.037863 0.042077 1.768345
18 Sweden 1.618274 2.01797 0.012056 0.01377 0.399696
19 Turkey 12.171312 6.355708 0.08065 0.048935 -5.815604
20 United_States 52.251121 54.521675 0.00846 0.007554 2.270554
In [69]:
# see the risk distribution
G_temp = G_nxs_feature['20190331']

def disparity_filter(G, alpha):
    s = G.out_degree(weight = 'claims_held')
    k = G.out_degree(weight = None)

    def pij(i, j):
        w = G.edges[i, j]['claims_held']
        return ((1 - (w / s[i])) ** (k[i] - 1)) < alpha

    return nx.subgraph_view(G, filter_edge = pij)


G_filt = disparity_filter(G_temp, .1)
print('Filtered network:', len(G_filt.edges), 'edges remain out of', len(G_temp.edges))

plt.figure(3, figsize = (10, 20))
plt.subplot(2, 1, 1)
plt.title('Inherent Risk')
nx.draw(
  G_filt,
  pos = nx.circular_layout(G_filt),
  node_size=1500,
  node_color = [wgt for _, wgt in G_filt.nodes.data('inherent_risk')],
  cmap = mpl.cm.coolwarm,
  with_labels = True,
  font_color = 'black',
  font_size = 10,
  edge_color = [np.log(wgt) for _, _, wgt in G_filt.edges.data('claims_held')],
  edge_cmap = mpl.cm.coolwarm,
  arrowsize = 15,
  connectionstyle="arc3,rad=0.1")

plt.subplot(2, 1, 2)
plt.title('Propagated Risk')
nx.draw(
  G_filt,
  pos = nx.circular_layout(G_filt),
  node_size=1500,
  node_color = [wgt for _, wgt in G_filt.nodes.data('propagated_risk')],
  cmap = mpl.cm.coolwarm,
  with_labels = True,
  font_color = 'black',
  font_size = 10,
  edge_color = [np.log(wgt) for _, _, wgt in G_filt.edges.data('claims_held')],
  edge_cmap = mpl.cm.coolwarm,
  arrowsize = 15,
  connectionstyle="arc3,rad=0.1")
plt.show()

Filtered network: 61 edges remain out of 407
In [70]:
pd.DataFrame({
    'inherent_risk': [id for id,  wgt in sorted(G_filt.nodes.data('inherent_risk'), key = lambda p: -p[1])][:15],
    'propagated': [id for id,  wgt in sorted(G_filt.nodes.data('propagated_risk'), key = lambda p: -p[1])][:15]
}).T
Out[70]:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
inherent_risk Canada Spain Japan Switzerland France Netherlands Sweden Germany United_Kingdom Italy Greece Austria Australia Finland United_States
propagated United_Kingdom Germany Spain Finland France United_States Austria Netherlands Switzerland Ireland Canada Italy Sweden Greece Australia
In [71]:
print(G_nxs_feature['20190331'].nodes['Canada'])
print(G_nxs_feature['20210331'].nodes['Canada'])
print(G_nxs_feature['20190331'].nodes['Portugal'])
print(G_nxs_feature['20210331'].nodes['Portugal'])
print(G_nxs_feature['20190331'].nodes['United_States'])
print(G_nxs_feature['20210331'].nodes['United_States'])

{'inherent_risk': 3.3381755613391912, 'propagated_risk': 0.04460473905587458}
{'inherent_risk': 3.279436230223105, 'propagated_risk': 0.04292556774093095}
{'inherent_risk': 0.3078149345402036, 'propagated_risk': 0.03457135581398739}
{'inherent_risk': 0.30144023477885445, 'propagated_risk': 0.03807989137416631}
{'inherent_risk': 0.34856712915498195, 'propagated_risk': 0.055509450386075215}
{'inherent_risk': 0.3604048114384204, 'propagated_risk': 0.05387045039652726}

Dynamic Analysis¶

Inherent and Propagated Risks¶

In [72]:
G_origin = G_nxs_feature['20210331']
G_remove = G_origin.copy()
In [73]:
G_remove.remove_node('Japan')
G_remove.remove_node('Canada')
G_remove.remove_node('Spain')
G_remove.remove_node('Switzerland')
G_remove.remove_node('Netherlands')
In [74]:
print("nodes: ", nx.number_of_nodes(G_remove))
print("edges: ", nx.number_of_edges(G_remove))

nodes:  17
edges:  241
In [75]:
# recalculate: lose out-strength, with old in-strength
print("***process")
in_strength = G_origin.in_degree(weight = 'claims_held')
out_strength = G_remove.out_degree(weight = 'claims_held')
# add norm
for src, tar, wgt in G_remove.edges.data('claims_held'):
    G_remove.edges[src, tar]['claims_held_norm'] = wgt / out_strength[src]
    G_remove.edges[src, tar]['claims_held_norm_reciprocal'] = 1 / G_remove.edges[src, tar]['claims_held_norm']
# add inherent risk
for node in list(G_remove.nodes(data=False)):
    G_remove.nodes[node]['inherent_risk'] = in_strength[node] / out_strength[node]
# add propagated risk
propagated_risk = nx.pagerank(G = G_remove.reverse(), # The borrower has higher risk, so change the direction
                                  nstart = dict(G_remove.nodes.data('inherent_risk')),
                                  weight = 'claims_held_norm')
for node in list(G_remove.nodes(data=False)):
    G_remove.nodes[node]['propagated_risk'] = propagated_risk[node]
nx.write_graphml_lxml(G_remove, "20210331_remove.graphml")
print("***finish")

***process
***finish
In [76]:
def disparity_filter(G, alpha):
    s = G.out_degree(weight = 'claims_held')
    k = G.out_degree(weight = None)

    def pij(i, j):
        w = G.edges[i, j]['claims_held']
        return ((1 - (w / s[i])) ** (k[i] - 1)) < alpha

    return nx.subgraph_view(G, filter_edge = pij)


G_filt = disparity_filter(G_remove, .1)
print('Filtered network:', len(G_filt.edges), 'edges remain out of', len(G_remove.edges))

plt.figure(3, figsize = (10, 20))
plt.subplot(2, 1, 1)
plt.title('Inherent Risk')
nx.draw(
  G_filt,
  pos = nx.circular_layout(G_filt),
  node_size=1500,
  node_color = [wgt for _, wgt in G_filt.nodes.data('inherent_risk')],
  cmap = mpl.cm.coolwarm,
  with_labels = True,
  font_color = 'black',
  font_size = 10,
  edge_color = [np.log(wgt) for _, _, wgt in G_filt.edges.data('claims_held')],
  edge_cmap = mpl.cm.coolwarm,
  arrowsize = 15,
  connectionstyle="arc3,rad=0.1")

plt.subplot(2, 1, 2)
plt.title('Propagated Risk')
nx.draw(
  G_filt,
  pos = nx.circular_layout(G_filt),
  node_size=1500,
  node_color = [wgt for _, wgt in G_filt.nodes.data('propagated_risk')],
  cmap = mpl.cm.coolwarm,
  with_labels = True,
  font_color = 'black',
  font_size = 10,
  edge_color = [np.log(wgt) for _, _, wgt in G_filt.edges.data('claims_held')],
  edge_cmap = mpl.cm.coolwarm,
  arrowsize = 15,
  connectionstyle="arc3,rad=0.1")
plt.show()

Filtered network: 39 edges remain out of 241
In [77]:
pd.DataFrame({
    'inherent_risk_before_deletion': [(id, wgt) for id,  wgt in sorted(G_origin.nodes.data('inherent_risk'), key = lambda p: -p[1])][:10],
    'inherent_risk_after_deletion': [(id, wgt) for id,  wgt in sorted(G_remove.nodes.data('inherent_risk'), key = lambda p: -p[1])][:10],
    'propagated_risk_before_deletion': [(id, wgt) for id,  wgt in sorted(G_origin.nodes.data('propagated_risk'), key = lambda p: -p[1])][:10],
    'propagated_risk_after_deletion': [(id, wgt) for id,  wgt in sorted(G_remove.nodes.data('propagated_risk'), key = lambda p: -p[1])][:10]
})
Out[77]:
inherent_risk_before_deletion inherent_risk_after_deletion propagated_risk_before_deletion propagated_risk_after_deletion
0 (Canada, 3.279436230223105) (France, 2.819779165253216) (United_Kingdom, 0.0692381146915677) (United_Kingdom, 0.09543567721705071)
1 (Spain, 2.8982666368586854) (Sweden, 2.220080819270625) (Spain, 0.06850635252576369) (Greece, 0.08241168605425063)
2 (Japan, 2.871092610464302) (Greece, 2.082681121519881) (Greece, 0.05982975073514005) (Germany, 0.07645097147100623)
3 (Switzerland, 2.4237244451641877) (United_Kingdom, 1.8783333937463362) (Germany, 0.0584028473434621) (France, 0.07594001298782484)
4 (Netherlands, 2.006200687678921) (Italy, 1.2450947577997007) (France, 0.055099320772883945) (United_States, 0.07315915235061783)
5 (France, 1.8393602113378291) (Germany, 1.1689268482463466) (Finland, 0.05503877576059898) (Portugal, 0.06666071637125452)
6 (Greece, 1.744085786388376) (Portugal, 1.0881602905207552) (Netherlands, 0.05492860343159948) (Italy, 0.06503683206275343)
7 (Sweden, 1.6880519661675164) (United_States, 1.081108193987226) (United_States, 0.05387045039652726) (Finland, 0.06452570694165613)
8 (United_Kingdom, 1.012396006676269) (Australia, 1.0509549081343135) (Ireland, 0.04995740986990863) (Ireland, 0.06297460599915577)
9 (Italy, 0.9163581915535357) (Austria, 0.7027345048263981) (Austria, 0.048390898919203604) (Austria, 0.05891658977795809)

Communities¶

In [78]:
G_temp = gt.load_graph("20210331_remove.graphml")
In [79]:
entropys = []
states = []
for i in range(10):
    state = gt.minimize_nested_blockmodel_dl(G_temp,
              state_args=dict(recs=[G_temp.properties[('e', 'claims_held')]], rec_types=["real-exponential"]))
    entropys.append(state.entropy())
    states.append(state)
pd.DataFrame({'entropys': entropys}).describe()
Out[79]:
entropys
count 10.000000
mean 1068.025150
std 37.999594
min 1050.155279
25% 1050.155279
50% 1052.570679
75% 1066.777471
max 1172.854414
In [80]:
index = np.argmin(entropys)
print(index)
print(entropys[index])
states[index].draw(vertex_text = G_temp.properties[('v', '_graphml_vertex_id')],
              vertex_size = 10)

1
1050.1552793425947
Out[80]:
(<VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc8090e59a0, at 0x7fc8091f8eb0>,
 <GraphView object, directed, with 23 vertices and 22 edges, edges filtered by (<EdgePropertyMap object with value type 'bool', for Graph 0x7fc8091f82e0, at 0x7fc809260be0>, False), vertices filtered by (<VertexPropertyMap object with value type 'bool', for Graph 0x7fc8091f82e0, at 0x7fc809260f40>, False), at 0x7fc8091f82e0>,
 <VertexPropertyMap object with value type 'vector<double>', for Graph 0x7fc8091f82e0, at 0x7fc809260eb0>)
In [81]:
G_filt.out_edges('Portugal', data = 'claims_held_norm')
Out[81]:
OutEdgeDataView([('Portugal', 'Germany', 0.18101038635767505), ('Portugal', 'France', 0.5085975156715764)])
In [82]:
G_filt.out_edges('Ireland', data = 'claims_held_norm')
Out[82]:
OutEdgeDataView([('Ireland', 'France', 0.1834157925779371), ('Ireland', 'United_Kingdom', 0.24105556326413083), ('Ireland', 'United_States', 0.3195601801260412)])

End¶